6th Grade - Gateway 1

The instructional materials reviewed for Eureka Grade 6 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 6 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 1, Mid-Module Assessment: Students identify the ratio and choose an appropriate model to explain (6.RP.3). Question 2 states, “Wells College in Aurora, New York was previously an all-girls college. In 2005, the college began to allow boys to enroll. By 2012, the ratio of boys to girls was 3 to 7. If there were 200 more girls than boys in 2012, how many boys were enrolled that year? Use a table, graph, or tape diagram to justify your answer.”
• In Module 1, End-of-Module Assessment: Students solve unit rate problems involving unit pricing and constant speed. Unit rates are limited to non-complex fractions (6.RP.3b). Question 4 states, “Your mother takes you to your grandparents’ house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives for another 30 minutes at constant speed of 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?”
• In Module 2, Mid-Module Assessment: Students solve a word problem involving division of a fraction by a fraction to determine the number of people that can be served 19½ pints of ice cream if each person is served ¾ of a pint (6.NS.1).
• In Module 3, End-of-Module Assessment: Students name positive and negative integers (6.NS.5,6a). Question 1 states, “Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a computer program. Mr. Kindle receives a daily email that updates him on all his transactions from the previous day. This morning, his email read as follows: Good morning, Mr. Kindle, Yesterday’s investment activity included a loss of $800, a gain of $960, and another gain of $230. Log in now to see your current balance. a. Write an integer to represent each gain and loss.”
• In Module 4, Mid-Module Assessment: Students express the perimeter of a patio in terms of ????, first using addition and then using multiplication, and use substitution to determine if the two expressions are equivalent (6.EE.2a-c,4).

The instructional materials reviewed for Eureka Grade 6 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 6.RP and 6.EE as well as clusters A and C in 6.NS.

• 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 six modules, Modules 1, 3 and 4 focus on major work. Modules 2 and 5 contain lessons related to the major work.
• Of the 180 days, 120 days (67 percent) are spent on major clusters of the grade.

The instructional materials reviewed for Eureka Grade 6 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 2, Topic B: 6.NS.3 supports the major work of 6.EE.3. Students build fluency in using the distributive property as they solve multiplication problems involving decimals. This supports their work in applying the distributive property to generate equivalent expressions.
• In Module 5, Topic B: 6.NS.8 supports the major work of 6.G.3. Students build fluency in finding the distance between points on a coordinate plane while applying this knowledge to determine distance, perimeter and area on the coordinate plane.
• In Module 5, Topic D: 6.G.4 supports the major work of 6.EE.1. Students determine the surface area of a right rectangular prism while writing expressions
• In Module 6, Lessons 9-11: 6.SP.5c supports the major work of 6.RP.5-6. Students determine Mean Absolute Value while using signed numbers.

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

All lessons are paced to be 45 minutes in length. Information on how to customize lessons is included at the beginning of each module in the Preparing To Teach a Lesson section.

The instructional materials for Eureka Grade 6 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, and how the lessons support the progression of Grade 6 standards by explicitly stating connections to prior or future grades. For example:

• Module 1, Ratios and Unit Rates: “In this module, students are introduced to the concepts of ratio and rate. Their previous experience solving problems involving multiplicative comparisons, such as Max has three times as many toy cars as Jack, (4.OA.A.2) serves as the conceptual foundation for understanding ratios as a multiplicative comparison of two or more numbers used in quantities or measurements (6.RP.A.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 6 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 5 or from previous Grade 6 work are included for each module. An example from Module 1 is:

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions | 5.NF.3
• Convert like measurement units within a given measurement system 5.MD.1
• Geometry 5.G.1 | 5.G.2
• Graph points on the coordinate plane to solve real-world and mathematical problems 5.G.1 | 5.G.2
• Measurement and Data | 5.MD.1
• Number anand Operations - Fractions | 5.NF.3
• Operations and Algebraic Thinking | 4.OA.2
• Use the four operations with whole numbers to solve problems | 4.OA.2

The instructional materials for Eureka Grade 6 materials do not contain content from future grade levels. In places where the content might be confused with that of a future grade, explanations are provided, such as the one found in the Lesson Notes for Lesson 7 in Module 6 (page 77): “Notice that deviations are actually signed distances, but calculations involving signed numbers are not covered until Grade 7. Here students can rely on knowledge from Grade 6, Modules 3, 4 and 5, as they work with the unsigned distances above and below the mean. In Grade 6, Module 3, students identified zero as a balance point between opposites on a number line. In this module, students understand that the mean balances total distances to the left of the mean and to the right of the mean on the number line.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Most lessons contain a “Problem Set” which are questions and word problems that focus on the standards of the lesson. In Module 5, Lesson 13, Problem Set Question 4 states, “Determine the volume of a cube with a side length of 5 ⅓ inches.” Students find the volume of a right rectangular prism with fractional edge lengths (6.G.2).

Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 3, Lesson 1, Exit Ticket Question 2 states, “Below is a list of numbers in order from least to greatest. Use what you know about the number line to complete the list of numbers by filling in the blanks with the missing integers. -6, -5, __, -3, -2, -1, __, 1, 2, __, 4, __, 6.” Students develop the concept of positive and negative numbers on a number line and real-life applications (6.NS.5).

The instructional materials for Eureka Grade 6 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, Lesson 1: “Ratios” is visibly shaped by 6.RP.A, “Understand ratio concepts and use ratio reasoning to solve problems.”
• In Module 1, Lesson 16: “From Ratios to Rates” is visibly shaped by 6.RP.A, “Understand ratio concepts and use ratio reasoning to solve problems.”
• In Module 4, Topic G: “Solving Equations” is shaped by 6.EE.B, “Reason about and solve one-variable equations and inequalities.”
• In Module 4, Lesson 33: “From Equations to Inequalities” is shaped by 6.EE.B, “Reason about and solve one-variable equations and inequalities.”

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 14: 6.NS.A connects to 6.NS.B as students use their understanding of division of fractions to develop an algorithm for dividing decimals.
• In Module 3, Lesson 19: 6.G.A connects to 6.NS.C as students determine that the length of a line segment drawn on a coordinate plane is the distance between its endpoints. They use this information to solve problems involving side lengths and areas of rectangles and triangles.
• In Module 4, Lesson 18: 6.EE.A connects to 6.EE.B when students understand mathematical language (sum, difference, etc.) to write expressions for real situations.
• In Module 6, Lesson 10: 6.NS.B connects to 6.SP.B as students describe a distribution involving decimals using the mean and mean absolute value.
• In Module 6, Lesson 16: 6.EE connects to 6.SP when students use variables and expressions to solve for quartiles. “A formula for the IQR could be written as Q3 - Q1 = IQR. Suppose you knew the IQR and and the Q1. How could you find the Q3?”