4th Grade - Gateway 1

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."

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.

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?”

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.

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).

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?”