8th Grade - Gateway 1

The instructional materials reviewed for Eureka Grade 8 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 8 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 1, Mid-Module Assessment: Students use their knowledge of prime numbers and apply the properties of integer exponents to generate an expression equivalent to a given expression (8.EE.1). Question 2 states, “Let m be a whole number. Use the properties of exponents to write an equivalent expression that is a product of unique primes, each raised to an integer power. 6 to the 21st power multiplied by 10 to the 7th power divided by 30 to the 7th power.”
• In Module 4, End-of-Module Assessment: Students solve a system of equations (8.EE.8). Question 5 states, “Students sold 275 tickets for a fundraiser at school. Some tickets are for children and cost $3, while the rest are adult tickets that cost $5. If the total value of all tickets sold was $1,025, how many of each type of ticket was sold?”
• In Module 7, Mid-Module Assessment: Students evaluate square roots and cube roots of perfect squares (8.EE.2). In Questions 6c and 6d, students use their knowledge of solving linear equations to write equations of the form $$x^2=p$$, equivalent to the given equations. While solving quadratic equations, in general, aligns to standards beyond Grade 8, these problems are aligned to grade-level standards (8.EE.2, 8.EE.8). Question 6d states, “Determine the positive solution for each of the following equations. $$x^3+3x-9=x-1+2x$$”
• In Module 7, End-of-Module Assessment: Students find the length of the hypotenuse of a right triangle when the area and the length of one side are known (8.G.7). Question 1c states, “The area of the right triangle shown below is 30 feet squared. The segment XY has a length of 5 ft. Find the length of the hypotenuse.”

The instructional materials reviewed for Eureka Grade 8 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 8.EE and 8.F as well as clusters A and B in 8.G.

• 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 seven modules, Modules 1-4 focus on major work. Modules 5, 6, and 7 contain lessons related to the major work of the grade.
• Of the 180 days, 146 days (81 percent) are spent on major work of the grade. The remaining lessons also make specific connections to the major work.

The instructional materials reviewed for Eureka Grade 8 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 5, Lesson 9: 8.G.9 supports the major work of 8.F. Students write a function to calculate an area of a partial space. Classwork Question 4 states, “Write a function that would allow you to calculate the area of a 1-inch white border for any sized square picture measured in inches.”
• In Module 6, Lesson 11: 8.SP.2-3 supports the major work of 8.F.4. Students create a linear prediction model from a scatter plot. Classwork Exercise 1 Question 1c states, “Suppose that Chang believes the variables to be linearly related. Use the first and last data points in the table to create a linear prediction model.”
• In Module 7, Lesson 1: 8.G.C supports the major work of 8.G.B. In Exercise 3, students use the Pythagorean theorem to find the slant height of a cone.
• In Module 7, Lesson 1: 8.NS.A supports the major work of 8.G.B. In Problem Set Question 1, students use the Pythagorean theorem to estimate the length of the unknown side of a right triangle.

Instructional materials for Eureka Grade 8 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: 20 days
• Module 2: 25 days
• Module 3: 25 days
• Module 4: 40 days
• Module 5: 15 days
• Module 6: 20 days
• Module 7: 35 days

All lessons are paced to be 45 minutes in length. Information on how to customize lessons is included in the Preparing To Teach A Lesson section.

The instructional materials for Eureka Grade 8 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 8 standards by explicitly stating connections to prior or future grades. For example:

• Module 4, Linear Equations: “In Module 4, students extend what they already know about unit rates and proportional relationships (6.RP.A.2, 7.RP.A.2) to linear equations and their graphs. Students understand the connections between proportional relationships, lines and linear equations in this module (8.EE.B.5, 8.EE.B.6). Also, students learn to apply the skills they acquired in Grades 6 and 7 with respect to symbolic notation and properties of equality (6.EE.A.2, 7.EE.A.1, 7.EE.B.4) to transcribe and solve equations in one variable and then in two variables.”

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 8 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 7 or from previous Grade 8 work are included for each module. An example from Module 1 is:

• Apply and extend previous understandings of arithmetic to algebraic expressions 6.EE.1
• Expressions and Equations 6.EE.1
• Geometry 7.G.6 | 7.G.4
• Number and Operations in Base Ten 5.NBT.2
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume 7.G.6 | 7.G.4
• Understand the place value system 5.NBT.2

The instructional materials for Eureka Grade 8 contain content from future grade levels that is identified and explanations are provided. Module 6, Lesson 12 begins with a note explaining why the optional lesson has been included in the Grade 8 materials. A similar explanation appears at the beginning of Lesson 4 in Module 7. Lesson 5 in Module 7 contains two problems that address content from future grades and are labeled as Challenge Problems 9-10.

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 include questions and word problems that focus on the standards of the lesson. In Module 5, Lesson 7, Problem Set Question 1 states, “The graph below represents the distance in miles, y, Car A travels in x minutes. The table represents the distance in miles, y, Car B travels in x minutes. It is moving at a constant rate. Which car is traveling at a greater speed? How do you know?” Students compare the properties of two functions (8.F.2).

Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 1, Lesson 10, Exit Ticket Question 1 states, “The speed of light is 3 x 10 to the 8th power meters per second. The sun is approximately 230,000,000,000 meters from Mars. How many seconds does it take for sunlight to reach Mars?” Students use operations with numbers in Scientific Notation to solve problems (8.EE.4).

The instructional materials for Eureka Grade 8 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: “Exponential Notation and Properties of Integer Exponents” is visibly shaped by 8.EE.A, “Expressions and equations work with radicals and integer exponents.”
• In Module 5, Topic A: “Functions” is visibly shaped by 8.F.A, “Define, evaluate and compare functions.”

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 4, Lesson 15: 8.G.A connects to 8.EE.A when students use similar triangles to explain why slope is the same between any two distinct points on a non-vertical line in the coordinate plane.
• In Module 4, Lesson 31: 8.EE.C connects to 8.G.B when students use a system of equations to find Pythagorean triples.
• In Module 4, Optional Topic E: 8.EE.C connects to 8.G.B when students learn about the Babylonian method for finding Pythagorean triples which requires an understanding and use of a system of linear equations.
• In Module 5, Lesson 9: 8.F.A connects to 8.G.A when students write rules to express functions related to geometry. “Write a function that would allow you to calculate the area of an 11-inch white border for any-sized square pictures measured in inches.”
• In Module 5, Lesson 9, Exercise 4: 8.F.A connects to 8.G.C as students write rules to express functions related to geometry.
• In Module 5, Lesson 10: 8.G.C connects to 8EE.B as students use proportional reasoning to develop the formula for the volume of a cone.