5th Grade - Gateway 1

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

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

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

The instructional materials reviewed for Eureka Grade 5 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 5.NBT and 5.NF as well as cluster C in 5.MD.

• More than 65 percent of the lessons are explicitly focused on major work, with major work often included within supporting work lessons as well.
• Of the 140 lesson days, approximately 110 days (79 percent) are spent on major clusters of the grade.
• Of six modules, Modules 1, 2, 3, 4 and 5 focus on major work with only a few lessons devoted to additional and supporting work.
• Module 6 consists of additional and supporting work with a few major work lessons included.
• Of the 31 assessment days, 22 are devoted to major work.

The instructional materials reviewed for Eureka Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade. For example:

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

Instructional materials for Eureka Grade 5 meet expectations that the amount of content designated for one grade level is viable for one year. As designed, the instructional materials can be completed in 180 days. The suggested amount of time and expectations of the materials for teachers and students are viable for one school year as written and would not require significant modifications.

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

• Module 1: 20 days
• Module 2: 35 days
• Module 3: 22 days
• Module 4: 38 days
• Module 5: 45 days
• Module 6: 25 days

All lessons are paced to be 60 minutes in length. Lessons generally include fluency practice, application problems, concept development and a student debrief. Lessons vary in amount of time spent on various sections but time estimates are reasonable and appropriate for the activities described. Module 6 includes 14 days for Multi-Step Word Problems and The Year in Review that include culminating activities and preparation for summer practice.

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

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

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

Each module has a “Module Standards” section that contains tabs named “Focus Grade-Level Standards” and “Foundational Standards”. The Focus Grade-Level Standards tab contains Grade 5 standards that are covered within the module. The Foundational Standards tab contains prior grade-level standards as well as grade-level standards that are the foundational skills needed for the lessons within the module. Foundational standards from Grade 3 or 4 as well as from previous Grade 5 work are included for each module. An example from Module 5 is:

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

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

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

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

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

The instructional materials for Eureka Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

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

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

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. For example:

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