Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for Eureka Grade 4 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.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

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

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials for Eureka Grade 4 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 reviewed for Eureka Grade 4 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 4 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

  • In Module 2, End-of-Module Assessment Task: Students use the standard algorithm to add and subtract multi-digit whole numbers (4.NBT.4). Question 3 states, “Find the sum or difference. a. 493 km 43 m + 17 km 57 m. b. 25 kg 32 g – 23 kg 83 g. c. 100 L 99 mL + 2,999 mL.”
  • In Module 3, Mid-Module Assessment Task: Students illustrate and multiply a whole number of up to four digits by a one-digit whole number, using strategies based on place value (4.NBT.5). Question 1b states, “Draw an area model to solve the following. Find the value of the following expressions. 3 x 269.”
  • In Module 4, Mid-Module Assessment Task: Students draw line segments, points, rays, angles (including acute, right and obtuse), lines, and perpendicular and parallel lines (4.G.1). Question 1a states, “Draw 2 points, A and B.” Question 1g states, “Name an obtuse angle. You may have to draw and label another point.”
  • In Module 5, Mid-Module Assessment Task: Students explain why a fraction is equivalent to another fraction (4.NF.1). Question 6 states, d. “Express the number of remaining containers as a product of a whole number and a unit fraction. e. Six out of the eight fish they caught were trout. What is another fraction equal to 6 eighths? Write a number sentence, and draw a model to show the two fractions are equal."

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 4 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 4 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

  • In Module 2, End-of-Module Assessment Task: Students use the standard algorithm to add and subtract multi-digit whole numbers (4.NBT.4). Question 3 states, “Find the sum or difference. a. 493 km 43 m + 17 km 57 m. b. 25 kg 32 g – 23 kg 83 g. c. 100 L 99 mL + 2,999 mL.”
  • In Module 3, Mid-Module Assessment Task: Students illustrate and multiply a whole number of up to four digits by a one-digit whole number, using strategies based on place value (4.NBT.5). Question 1b states, “Draw an area model to solve the following. Find the value of the following expressions. 3 x 269.”
  • In Module 4, Mid-Module Assessment Task: Students draw line segments, points, rays, angles (including acute, right and obtuse), lines, and perpendicular and parallel lines (4.G.1). Question 1a states, “Draw 2 points, A and B.” Question 1g states, “Name an obtuse angle. You may have to draw and label another point.”
  • In Module 5, Mid-Module Assessment Task: Students explain why a fraction is equivalent to another fraction (4.NF.1). Question 6 states, d. “Express the number of remaining containers as a product of a whole number and a unit fraction. e. Six out of the eight fish they caught were trout. What is another fraction equal to 6 eighths? Write a number sentence, and draw a model to show the two fractions are equal."

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 reviewed for Eureka Grade 4 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 4.NBT and 4.NF as well as cluster A in 4.OA.

  • 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 151 lesson days, approximately 128 days (85 percent) are spent on the major clusters of the grade.
  • Of the seven modules, Module 1 focuses on major work. Modules 2, 3, 5, 6 and 7 devote a few lessons to additional and supporting work.
  • Module 4 focuses on additional and supporting work.
  • Of the 27 assessment days, 18 are devoted to major work.

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 4 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 4.NBT and 4.NF as well as cluster A in 4.OA.

  • 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 151 lesson days, approximately 128 days (85 percent) are spent on the major clusters of the grade.
  • Of the seven modules, Module 1 focuses on major work. Modules 2, 3, 5, 6 and 7 devote a few lessons to additional and supporting work.
  • Module 4 focuses on additional and supporting work.
  • Of the 27 assessment days, 18 are devoted to major work.

Criterion 1c - 1f

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

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 4 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 3, 4.MD.3 supports the major work cluster 4.OA.A. Students use the four operations to solve real-world problems involving area and perimeter. Problem Set Question 4 states, “The length of a rectangular deck is 4 times its width. If the deck’s perimeter is 30 feet, what is the deck’s area?”
  • In Module 5, Lesson 28, 4.MD.B supports the major work cluster 4.NF.A. Students use fractions while working with line plots. Problem Set Questions 2 and 3 state, “Solve each problem. a. Who ran a mile farther than Jenny? b. Who ran a mile less than Jack? c. Two students ran exactly 2 1/4 miles. Identify the students. How many quarter miles did each student run? d. What is the difference, in miles, between the longest and shortest distance run? e. Compare the distances run by Arianna and Morgan using >, <, or =. f. Ms. Smith ran twice as far as Jenny. How far did Ms. Smith run? Write her distance as a mixed number. g. Mr. Reynolds ran 1 3/10 miles. Use >, <, or = to compare the distance Mr. Reynolds ran to the distance that Ms. Smith ran. Who ran farther?” and “Using the information in the table and on the line plot, develop and write a question similar to those above. Solve, and then ask your partner to solve. Did you solve in the same way? Did you get the same answer?”
  • In Module 5, Lesson 41, 4.OA.5 supports the major work standard 4.NF.3a. Students analyze and compare the patterns created when adding fractions with even and odd denominators. Problem Set Question 2 states, “Describe a pattern you notice when adding the sums of fractions with even denominators as opposed to those with odd denominators.”
  • In Module 6, Lesson 9, 4.MD.2 supports the major work standard 4.NF.7. Students solve word problems involving addition of measurements in decimal form. Problem Set Question 3 states, “An apple orchard sold 140.5 kilograms of apples in the morning and 15.85 kilograms more apples in the afternoon than in the morning. How many total kilograms of apples were sold that day?”

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 4 meet expectations that the amount of content designated for one grade level is viable for one year. As designed, the instructional materials can be completed in 180 days. The suggested amount of time and expectations of the materials for teachers and students are viable for one school year as written and would not require significant modifications.

The instructional materials consist of seven modules. Instruction and assessment days are included in the following count:

  • Module 1: 25 days
  • Module 2: 7 days
  • Module 3: 43 days
  • Module 4: 20 days
  • Module 5: 45 days
  • Module 6: 20 days
  • Module 7: 20 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 7 includes four days for 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 4 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 4 standards by explicitly stating connections to prior or future grades. For example:

  • Module 2, Unit Conversions and Problem Solving with Metric Measurement: “In Topic A, students review place-value concepts while building fluency with decomposing, or converting from larger to smaller units (4.MD.1). They learn the relative sizes of measurement units, building off prior knowledge of grams and kilograms from Grade 3 (3.MD.2) and meters and centimeters from Grade 2 (2.MD.3). Conversions between the units are recorded in a two-column table. Single-step problems involving addition and subtraction of metric units provide an opportunity to practice mental math calculations as well as the addition and subtraction algorithms established in Module 1.”

Each module has a “Module Standards” section that contains tabs named “Focus Grade-Level Standards” and “Foundational Standards”. The Focus Grade-Level Standards tab contains Grade 4 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 from previous Grade 4 work are included for each module. An example from Module 2 is:

  • Measurement and Data 2.MD.5 | 3.MD.2
  • Number and Operations in Base Ten 2.NBT.1 | 4.NBT.4
  • Operations and Algebraic Thinking 4.OA.3
  • Relate addition and subtraction to length. 2.MD.5
  • Solve problems involving measurement and estimation. 3.MD.2
  • Understand place value. 2.NBT.1
  • Use place-value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4
  • Use the four operations with whole numbers to solve problems. 4.OA.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 2, Lesson 2, the Fluency Practice focuses on standards 4.MD.1 and 4.MD.2. Convert Units, Unit Counting, and Add and Subtract Meters and Centimeters is the focus of the 12-minute fluency practice.
  • In Module 4, Lesson 6, the Fluency Practice focuses on standards 4.NBT.6 and 4.G.1. Divide Using the Area Model, Draw and Identify Two-Dimensional Figures, and Physiometry 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 9, Problem Set Problem 7 states, “A small bag of chips weighs 48 grams. A large bag of chips weighs three times as much as the small bag. How much will 7 large bags of chips weigh?” Students solve multi-step word problems with whole numbers (4.OA.3).

Most lessons contain an “Exit Ticket” that contains grade-level problems that focus on the standards taught in the lesson. In Module 6, Lesson 4, Exit Ticket Question 1 states, “Shade in the amount shown. Then, write the equivalent decimal 6/10 m.” Students use decimal notation for fractions with denominators of 10 or 100 (4.NF.6).

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 4 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. For example:

  • In Module 1, Topic A: "Place Value of Multi-digit Whole Numbers" is visibly shaped by 4.NBT.A, "Generalize place-value understanding for multi-digit whole numbers."
  • In Module 2, Topic A: “Metric Unit Conversions" is visibly shaped by 4.MD.A, "Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit."
  • In Module 5, Topic A: "Decomposition and Fraction Equivalence," is visibly shaped by 4.NF.A, "Extend understanding of fraction equivalence and ordering."

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 3, Lesson 2: 4.OA.A connects to 4.MD.A when students solve real-world problems involving perimeter. Problem Set Question 4 states, “The area of Betsy’s rectangular sandbox is 20 square feet. The longer side measures 5 feet. The sandbox at the park is twice as long and twice as wide as Betsy’s. a. Draw and label a diagram of Betsy’s sandbox. What is its perimeter?” b. “Draw and label a diagram of the sandbox at the park. What is its perimeter?”
  • In Module 5, Lesson 28: 4.NF.B connects to 4.MD.A when students subtract fractions to solve a problem involving measurement. Homework Question 2d states, “What is the difference, in inches, between Lilia’s and Martha’s shoe lengths?”

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials for Eureka Grade 4 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 4 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 4 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade level. For example:

  • In Module 1, Lesson 1, students develop conceptual understanding of a multiplication equation as a comparison. The teacher is prompted to facilitate student discussion by saying, “T: Discuss the patterns you have noticed with your partner. S: 10 ones make 1 ten. 10 tens make 1 hundred. 10 hundreds make 1 thousand. Every time we get 10, we bundle and make a bigger unit. We copy a unit 10 times to make the next larger unit. If we take any of the place value units, the next unit on the left is ten times as many.” (4.NBT.A)
  • In Module 1, Lesson 8, students develop conceptual understanding of rounding to a place value. A vertical number line is used to model rounding to a place value. Problem Set Question 1 states, “Complete each statement by rounding the number to the given place value. Use the number line to show your work. 1a. 53,000 rounded to the nearest ten thousand is _______.” (4.NBT.3)
  • In Module 3, Lesson 16, students develop conceptual understanding of division with a remainder. Students use place-value disks to solve two-digit dividend division problems with a remainder in the ones place. The teacher is prompted to facilitate student discussion by saying, “T: (Point to the place value chart.) We divided 6 ones and have no ones remaining. 6 ones minus 6 ones equals 0 ones. (Write the subtraction line.) What does this zero mean? S: There is no remainder. All the ones were divided with none left over. We subtracted the total number distributed from the total number of ones. T: We can see the 3 groups of 2 both in our model and in our numbers and know our answer is correct since 3 times 2 equals 6.” (4.NBT.B)

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

  • In Module 1, Lesson 15, students independently demonstrate conceptual understanding of place value. Students use tape diagrams to demonstrate conceptual understanding of place value to solve word problems. Problem Set Question 2 states, “Use tape diagrams and the standard algorithm to solve the problems below. Check your answers. 2. David is flying from Hong Kong to Buenos Aires. The total flight distance is 11,472 miles. If the plane has 7,793 miles left to travel, how far has it already traveled?” (4.NBT.4)
  • In Module 4, Lesson 6, students independently demonstrate conceptual understanding of fractions. Students relate fractions as division to fraction of a set. The teacher is prompted to facilitate student discussion by saying, “T: Make an array with 6 counters turned to the red side, and use your straws to divide your array into 3 equal parts. T: Write a division sentence for what you just did. S: 6 ÷ 3 = 2. T: Rewrite your division sentence as a fraction, and say it aloud as you write it. S: (Write 6/3=2.) 6 divided by 3 equals 2. T: If I want to show 1 third of this set, how many counters should I turn over to yellow? Turn and talk.” (4.NF.B)
  • In Module 5, Lesson 20, students independently demonstrate conceptual understanding of fractions. Students use tape diagrams when adding fractions. Problem Set Question 1 states, “Use a tape diagram to represent each addend. Decompose one of the tape diagrams to make like units. Then, write the complete number sentence.” (4.NF.3)

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 4 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

In A Story of Units Curriculum Overview, 4.NBT.4 (fluently add and subtract multi-digit whole numbers using the standard algorithm), is addressed explicitly in Module 1. For example:

  • The Lesson 11 Problem Set students gain procedural skills with multi-digit addition problems using the standard algorithm.
  • In Lesson 13, students develop procedural skill and fluency of subtraction of multi-digit whole numbers.
  • In Lesson 16, students solve two-step word problems using the standard algorithm. Problem Set problem #2, “A gas station has two pumps. Pump A dispensed 241,752 gallons. Pump B dispensed 113,916 more gallons than Pump A. a. About how many gallons did both pumps dispense? Estimate by rounding each value to the nearest hundred thousand and then compute. b. Exactly how many gallons did both pumps dispense? C. Assess the reasonableness of you answer in (b). Use you estimate from (a) to explain.”

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

  • In Module 1, Lesson 5 students build fluency of multiplication by 4 during the Sprint.
  • In Module 5, Lesson 6 Sprint students build fluency with addition of whole numbers and unit fractions, and multiplication of unit fractions by whole numbers.
  • In Module 6, Lesson 13, students engage in Fluency Practice ordering decimal numbers, and writing in decimal and fraction notation.

    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 4 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

    The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level. For example:

    • In Module 1, Lesson 18, students engage in grade-level mathematics when using subtraction to solve a word problem. The Application Problem states, “In all, 30,436 people went skiing in February and January. 16,009 went skiing in February. How many fewer people went skiing in January than in February?” (4.NBT.4)
    • In Module 2, Lesson 3, students engage in grade-level mathematics when solving a word problem involving conversion of measurements and subtraction. The Application Problem states, “A liter of water weighs 1 kilogram. The Lee family took 3 liters of water with them on a hike. At the end of the hike, they had 290 grams of water left. How much water did they drink? Draw a tape diagram, and solve using an algorithm or a simplifying strategy.” (4.MD.2)
    • In Module 5, Lesson 13, students engage in grade-level mathematics when using equivalent fraction knowledge to solve word problems. The Application Problem states, “Mr. and Mrs. Reynolds went for a run. Mr. Reynolds ran for 6/10 mile. Mrs. Reynolds ran for 2/5 mile. Who ran farther? Explain how you know. Use the benchmarks 0, 1/2 , and 1 to explain your answer.” (4.NF.2)

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

    • In Module 3, Lesson 2, students independently demonstrate the use of mathematics by applying knowledge of area and perimeter to solve multiplicative comparison word problems. Problem Set Question 4 states, “The area of Betsey’s rectangular sandbox is 20 square feet. The longer side measures 5 feet. The sandbox at the park is twice as long and twice as wide as Betsy’s. a. Draw and label a diagram of Betsy’s sandbox. What is its perimeter? b. Draw and label a diagram of the sandbox at the park. What is its perimeter?” (4.OA.3)
    • In Module 5, Lesson 19, students independently demonstrate the use of mathematics by applying understanding of addition and subtraction of fractions to solve word problems. Problem Set Question 1 states, “Sue ran 9/10 mile on Monday and 7/10 mile on Tuesday. How many miles did Sue run in the 2 days?” (4.NF.3d)
    • In Module 5, Lesson 40, students independently demonstrate the use of mathematics by applying their knowledge of multiplication and fractions to solve real-world problems. Problem Set Question 3 states, “Six of the players on the team weigh over 300 pounds. Doctors recommend that players of this weight drink at least 3 3/4 quarts of water each day. At least how much water should be consumed per day by all 6 players?” (4.NF.4c)

    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 4 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 3, Lesson 7, students practice fluency of multi-digit multiplication. Sprint Question 5 states, “2 x 3,000 = ____”
    • In Module 5, Lesson 5, students develop conceptual understanding of equivalent fractions by decomposing rectangles. Problem Set Question 1 states, “Draw horizontal lines to decompose each rectangle into the number of rows indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence. 2 rows. 1/4 = 2/__, 1/4 = 1/8 + ___ = ___, 1/4 = 2 x ___ = ___.”
    • In Module 7, Lesson 4, students engage in the application of mathematics by solving word problems involving multiplicative comparison of measurement units. Problem Set Question 1 states, “Beth is allowed 2 hours of TV time each week. Her sister is allowed 2 times as much. How many minutes of TV can Beth’s sister watch?”

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

    • In Module 1, Lesson 10, students develop conceptual understanding of place value by solving real-world problems. Problem Set Question 3 states, “Empire Elementary School needs to purchase water bottles for field day. There are 2,142 students. Principal Vadar rounded to the nearest hundred to estimate how many water bottles to order. Will there be enough water bottles for everyone? Explain.”
    • In Module 3, Lesson 11, students develop conceptual understanding and practice fluency of multi-digit multiplication by using partial products and the area model to solve problems. Problem Set Question 1a states, “Solve the following expressions using the standard algorithm, the partial products method, and the area model. 425 x 4, 4 (400 + 20 + 5), (4 x ___) + (4 x ___) + (4 x ___).”
    • In Module 3, Lesson 32, students practice fluency of division by solving real-world problems. Problem Set Question 1 states, “A concert hall contains 8 sections of seats with the same number of seats in each section. If there are 248 seats, how many seats are in each section?”

    Criterion 2e - 2g.iii

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

    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 4 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 6, the explanation for MP 8 states, “Look for and express regularity in repeated reasoning. As they progress through this module, students have multiple opportunities to explore the relationships between and among units of ones, tenths, and hundredths. Relationships between adjacent place values, for example, are the same on the right side of the decimal point as they are on the left side, and students investigate this fact working with tenths and hundredths. Further, adding tenths and hundredths requires finding like units just as it does with whole numbers, such as when adding centimeters and meters. Students come to understand equivalence, conversions, comparisons, and addition involving decimal fractions.”

    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 4 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 1, Lesson 2, MP 1 is identified in the teacher edition and attends to the full meaning of the practice where students reason abstractly about place value and division to solve division problems.
    • In Module 3, Lesson 14, MP 4 is identified in the teacher edition and attends to the full meaning of the practice where students use tape diagrams to model their thinking while finding the solution to word problems involving division.
    • In Module 6, Lesson 12, MP 6 is identified in the teacher edition and attends to the full meaning of the practice where students are adding tenths and hundredths with sums greater than 1. Students attend to precision when converting tenths to hundredths. “T: Solve, and then explain your solution to your partner. (Two solution strategies are pictured below.) S: I changed 6 tenths to 60 hundredths and then made 1 by adding 50 hundredths, which I took out of each addend. That meant 10 hundredths and 7 hundredths were left to be added. The sum is 1 17/100. I just added 60 hundredths and 57 hundredths to get 117 hundredths and then decomposed to get 100 hundredths and 17 hundredths. I converted 6 tenths to 60 hundredths and then took out 40 hundredths from 57 hundredths to make 1 and added on the leftover 17 hundredths.”

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

    • In Module 3, Lesson 11, MP 5 is identified in the teacher edition where the students solve a multiplication problem. “T: “Solve 316 times 4 using the standard algorithm, and compare your answer to the area model. S: 316 times 4 is 1,264. I got that answer using both methods. The area model doesn’t let me show how to regroup 24 ones for 2 tens 4 ones, but the algorithm does. I can regroup in the area model. I can draw an arrow to regroup 20 ones as 2 tens. Now, my area model looks like a place-value chart because I regrouped to show 6 tens. The area model aligns better to the partial products method, but the algorithm is still the quickest way for me to solve!” This is an example of not attending to the full practice as students are told what strategy to use rather than selecting a strategy to solve a multiplication problem.
    • In Module 2, Lesson 3, MP 1 is identified in the teacher edition where the students solve an addition measurement problem. Students are told to use a tape diagram. Also, the teacher offers two ways of solving the problem, as stated:“T: Work with your partner to solve. Will you use a simplifying strategy or an algorithm? S: A simplifying strategy. I know that 300 milliliters + 700 milliliters is 1,000 milliliters. That brings us to 2 liters. Then, all I need to do is add 170 milliliters more. 700 mL + 170 mL = 870 mL.” This is an example of not attending to the full practice as students are given two choices of strategies to solve the problem. Students do not independently persevere in solving the problem.

    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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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 4, the materials prompt students to determine which multi-digit number is written in word form correctly and explain their analysis for their choice. Problem Set Question 4 states, “Black rhinos are endangered, with only 4,400 left in the world. Timothy read that number as “four thousand, four hundred.” His father read the number as “44 hundred.” Who read the number correctly? Use pictures, numbers, or words to explain your answer.”
    • In Module 1, Lesson 10, the materials prompt students to construct an argument stating why an answer can be the same when rounding a number to different place values. Exit Ticket Question 1 states, “There are 598,500 Apple employees in the United States. Round the number of employees to the given place value. Thousand: ___, ten thousand: ___, hundred thousand: ___. Explain why two of your answer are the same.”
    • In Module 4, Lesson 4, the materials prompt students to determine whether a statement about the attributes of a triangle is correct and construct a viable argument for their thinking. Problem Set Question 5 states, “True or false? A triangle cannot have sides that are parallel. Explain your thinking.”
    • In Module 5, Lesson 18, the materials prompt students to analyze two different strategies to add fractions and explain which strategy they like best. Problem Set Question 2 states, “Monica and Stuart used different strategies to solve 5/8 + 2/8 + 5/8. Whose strategy do you like best? Why?”

    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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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 4, Lesson 4, teachers are prompted to engage students in constructing an argument by asking students about the properties of a rectangle. “What do you notice about sides of a rectangle and parallel lines? Is this true for all rectangles? Does the length of the opposite sides of a rectangle change the fact that they are parallel?”
    • In Module 7, Lesson 5, teachers are prompted to encourage students to critique a partner's work. “T: Work with a partner to complete the Problem Set. When you are finished solving and creating a word problem to go along with each diagram, turn to your partner and share. Use the peer share and critique form to take notes about your work and your partner’s work.”
    • In Module 7, Lesson 12, teachers are prompted to engage students in constructing an argument by asking students to explain their alternative solution of finding an equivalent fraction other than using a tape diagram. “Talk to your partner. Instead of just using the tape diagram, how can we use what we know about finding equivalent fractions to find the number of twelfths equal to 1/2 foot? Again, how many inches are equal to 1/2 or 6/12 foot? Work with your partner to find how many inches are equal to 1/4 foot. (Allow students time to work.) How did you figure it out?”

    Indicator 2g.iii

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

    The instructional materials reviewed for Eureka Grade 4 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 5, Lesson 9, the Notes on Multiple Means of Expression states, “As the conceptual foundation for simplification is being set, the word simplify is initially avoided with students as they compose higher-value units. The process is rather referred to as composition, the opposite of decomposition, which relates directly to their drawing, work throughout the last two lessons, and work with whole numbers. When working numerically, the process is referred to at times as renaming, again in an effort to relate to whole number work.”
    • In Module 6, Lesson 9, the Notes on Terminology state, “Mass is a fundamental measure of the amount of matter in an object. While weight is a measurement that depends upon the force of gravity (one would weigh less on the moon than one does on Earth), mass does not depend upon the force of gravity. Both words are used here, but it is not important for students to recognize the distinction in mathematics at this time.”

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

    • In Module 2, Lesson 1, the mathematical term kilometer is in bold writing within a question listed in the Student Debrief section. These questions guide teachers in leading a class discussion. “What pattern did you notice in the equivalences for Problems 1 and 2 of the Problem Set? How did converting 1 kilometer to 1,000 meters in Problem 1(a) help you to solve Problem 2(a)?”
    • In Module 3, Lesson 22, the materials use accurate terminology and support students in using the term factor pairs. Problem Set Question 4 states, “Sheila has 28 stickers to divide evenly among 3 friends. She thinks there will be no leftovers. Use what you know about factor pairs to explain if Sheila is correct.”

    Gateway Three

    Usability

    Meets Expectations

    Criterion 3a - 3e

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

    The instructional materials for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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 5, Lesson 4, students decompose fractions into sums of smaller unit fractions using tape diagrams. Problem Set Question 3 states, “Draw and label tape diagrams to prove the following statements. The first one has been done for you. ⅖ = 4/10”

    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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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 12, students use a number line when comparing a given fraction to a benchmark fraction.

    Examples of manipulatives for Grade 4 include:

    • Meter Sticks
    • Rulers
    • Square Inch Tiles
    • Centimeter Cubes
    • 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
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    Indicator Rating Details

    The visual design in Eureka Grade 4 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
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    Criterion Rating Details

    The instructional materials for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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, “How did the Application Problem connect to today’s lesson with decimal fractions?”

    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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Criterion Rating Details

    The instructional materials for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The materials reviewed for Grade 4 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
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    Indicator Rating Details

    The instructional materials for Eureka Grade 4 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
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    Criterion Rating Details

    The instructional materials for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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
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    Indicator Rating Details

    The instructional materials reviewed for Eureka Grade 4 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 3aa - 3z

    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 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.

    Indicator 3ad

    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.

    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.

    Additional Publication Details

    Report Published Date: Mon Aug 27 00:00:00 UTC 2018

    Report Edition: 2015

    About Publishers Responses

    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.

    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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