8th Grade - Gateway 1

The instructional materials reviewed for Reveal Math Grade 8 meet expectations that they assess grade-level content. 

The materials provide three versions of the Module assessment which include a variety of Item types as well as a Performance Task for each Module. In addition, there are quarterly benchmark tests to show growth over the year. 

Examples of assessment items aligned to grade-level standards include:

• Module 3 Test Form A, Item 17: “Robin simplified both sides of an equation. The left side of the equation has the same coefficient, but a different constant than the right side of the equation. Explain how to determine the number of solutions of the equation.” (8.EE.7)
• Module 5 Test Form A, Item 17: “Mandy owns a car dealership in which her employees earn commission for each car they sell in addition to a weekly salary. One employee sells 5 cars and makes $1700 that week. A second employee sells 6 cars and makes $1940 that week. Part A) Write an equation, in slope-intercept form, for the amount of money (y) a salesman will make in a week given the number of cars they sell in a week x. Part B) How much will a salesman earn for selling 10 cars in one week?” (8.F.4)
• Module 8 Test Form C, Item 5: “The graph shows the movement of a baseball. The baseball moved from point B to point C to point A. Find the distance of the movement of the baseball. Round to the nearest tenth if necessary.” Each point is in a different quadrant. Students use the Pythagorean Theorem to find distance. (8.G.8)
• Benchmark Test 2, Item 1: “Retta won 4 times as many ribbons at the county fair as Ximena did. Ximena won 6 fewer ribbons than Retta. The number of ribbons won by each friend can be represented by this system of equations: y = 4x; y = x + 6. 
• Part A) Graph these equations on the coordinate plane. Plot the point of intersection.
• Part B) Complete true statements to identify and interpret the solution to the system of equations. The point of intersection is (__, __). So, Ximena won ___ ribbon(s); and Retta won ___ ribbon(s).” (8.EE.8)
• Module 6 Performance Task: “Part D) Keith and Margo decided to order a unique reclaimed barn wood door for the kitchen pantry. This unique item had to be shipped across the country. Keith tracked the door as it was being shipped. Over a 2-day period, the door had traveled a total distance of 1,140 miles during a 22-hour period of shipping. The first day the door was on a train that traveled at an average rate of 45 miles per hour, and on the second day the door was on a truck that traveled at an average rate of 60 miles per hour. Write and solve a system of equations to determine the number of hours the door was being shipped by train and the number of hours the door was being shipped by truck. You may solve using the method of your choice.” (8.EE.8)

Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. The materials are digital and download as a word document, making it easy to modify or omit Items. These items include:

Module 2 Test Form A, Item 8: “What is the value of g if the cube root of g = -7.” (A-REI.2)

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 out of 11, which is approximately 72%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 47 out of 57, which is approximately 82%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 129 out of 167.5, which is approximately 77%. 

A lesson level analysis is most representative of the instructional materials because lessons directly reflect the grade-level concepts identified for each lesson. In addition, teachers have flexibility in the length of time they may spend on different aspects of the lesson. As a result, approximately 82% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples of how the materials connect supporting standards to the major work of the grade include: 

• In Lesson 7-3, 8.NS.A supports 8.G.B as students use the Pythagorean Theorem to find missing side lengths to the nearest whole number or tenth using rational approximations. Practice Question 4 states, “The distance from the top of the cone to the edge is 15 feet. The height of the cone is 6 feet. What is the radius of the cone? Round to the nearest tenth.” Practice Question 1 states, “What is the length of a diagonal of a rectangular picture whose sides are 12 in. by 17 in.?” In Lesson 7-5, Practice Question 6 states, “The coordinates of points A and B are (-7,5) and (4, -3), respectively. What is the distance, in units, between the points? Round to the nearest tenth.”
• In Lesson 10-4, 8.G.C supports 8.EE.2 as students solve cylinder, cone, and sphere volume formulas to find missing dimensions. Practice Question 5 states, “Find the radius of a sphere with a volume of 26,244 cubic inches.” In Explore and Develop, Example 2 states, “The volume of a cone with a height of 6 inches is 8 cubic inches. What is the radius of the cone?”
• In Lesson 11-3, 8.SP.3 supports 8.F.4 and 8.EE.6 as students find equations for lines of best fit to analyze bivariate data. In Explore and Develop, Example 1 states, “The scatter plot shows the amount of time Mia spends practicing the piano and the number of mistakes made. Write an equation in slope-intercept form for the line of best fit that is drawn. Then interpret the slope and y-intercept.” Practice Question 5 states, “Suppose a sports analyst wants to compare the number of hits a baseball player has in a season to the number of runs they score, by graphing data on a scatter plot. How do you think you could use the slope and y-intercept of the line of fit to predict the number of runs a player would score based on a certain number of hits they have?”

The instructional materials for Reveal Math Grade 8 meet expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 167.5 days.

• The pacing guide is based on daily classes of 45 minutes. 
• Grade 8 includes 57 lessons which account for 121 instructional days.
• Each Module includes one review day and one assessment day for 22 days. The assessment could be a performance task or the module test.  
• Put It All Together are mid-module checkpoints which could be used as an assessment, a review, or homework which are each allocated a half-day of instruction. There are 19 Put It All Togethers for Grade 8, which leads to nine and a half days of instruction.
• There is one day allocated for Module introduction and pre-assessment, which is 11 days. 
• Each grade includes four benchmark assessments during the year. 
• Differentiation activities are not specified in the pacing guide.

The instructional materials for Reveal Math Grade 8 meet expectations for the materials being consistent with the progressions in the Standards. Off grade-level material is identified and is relevant to grade-level work; it does not interfere with the work of the grade. In addition, the instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.The instructional materials identify prior knowledge at both the module and lesson level in the vertical alignment.

In the Teacher Edition and the Vertical Alignment tab online, the introduction for each module includes a progression of concepts and standards across the grades. The beginning of each module states: “The mathematical content in this module connects with what students have previously learned and what they will learn in upcoming modules.” Vertical alignment is provided at both the module and lesson level using the format of previous-now-next. Many of the connections provided are within the current grade. For example:

• Module 2: ”Previous - Students studied the set of rational numbers. (6.NS.6, 7.NS.2d); Now - Students learn about the real number system by identifying, calculating, and estimating irrational numbers and comparing them to rational numbers. (8.NS.1,2, 8.EE.2); Next - Students study and use the properties of rational and irrational numbers. (N-RN.3)”
• Lesson 1-1: “Previous - Students used the order of operations to evaluate expressions without exponents. (7.NS.1d, 7.NS.2c, 7.EE.1); Now - Students write and evaluate expressions involving powers and exponents; Next - Students will use the Laws of Exponents to simplify expressions involving products and quotients of monomials. (8.EE.1)”

The materials provide all students the opportunity to engage with extensive, grade-level work. For example:

• The Correlation to Mathematical Standards document delineates the content, indicating that all grade-level standards are represented throughout the course.
• Each lesson includes grade level practice for all students in the Interactive Presentation, Explore, Apply, and optional Practice pages. Online, each lesson also includes Reflect and Practice which contains an Exit Ticket and Practice pages for student use. 
• In the Teacher Edition, each Module includes leveled discussion questions and differentiated practice questions to support all students with grade-level concepts.
• When work is differentiated, the materials continue to develop grade-level concepts. For example, in Lesson 7-5, the corresponding interactive review guides students to find positive square roots; the extension lesson provides the opportunity to find the area of a triangle using Heron’s Formula.
• There is opportunity for additional digital practice with every lesson. For each example or application in Explore and Develop, students are prompted to “Go Online” to complete an “Extra Example”.

Examples of grade-level work:

• Lesson 7-1: “In the figure, line m is parallel to line n. The measure of angle 3 is 58 degrees. What is the measure of angle 7?” (two transversals cross lines m and n) (8.G.5)
• Lesson 10-2: “A funnel is in the shape of a cone. The radius is 2 inches and the height is 4.6 inches. What is the volume of the funnel? Round to the nearest tenth?” (8.G.9)

The materials reference prior knowledge at both the Module and Lesson level. Standards are explicitly referenced in Vertical Alignment for several lessons. For example:

• In the Teacher’s Edition, the Warm Up exercises at the beginning of each Lesson list “prerequisite” topics related to current material. The skills are from previous grade-level lessons as well as previous grades. The materials do not explicitly identify when the skills are below grade level. For example, Lesson 1-1, Question 1: “Multiply. Write in simplest form: (-2)(-2)(-2).” This is not identified as previous learning (7.NS.2), but is identified as prerequisite knowledge. 
• Each module contains “Are You Ready?” and a Module Pretest which identify prior knowledge and diagnose student readiness. The materials do not explicitly identify the standards that are below grade level, though it is clear that this is previous learning. For example, in Module 4, the Pretest addresses subtracting integers and evaluating expressions as well as graphing on the coordinate plane.
• Each Module includes “Be Sure to Cover” for teachers that states, “Students need to have a thorough understanding of the prerequisite skills required for this module.” Then identifies 2-3 skills and provides the prompt, “Use the Module pretest to diagnose students’ readiness for this module. You may wish to spend more time on the Warm Up for each lesson to fully review these concepts.”
• In the Teacher’s Edition, the Warm Up exercises at the beginning of each Lesson list “prerequisite” topics related to current material. The skills are from previous grade-level lessons as well as previous grades. The materials do not explicitly identify when the skills are below grade level. For example, Lesson 1-1, Question 1: “Multiply. Write in simplest form: (-2)(-2)(-2).”  This is not identified as previous learning (7.NS.2), but is identified as prerequisite knowledge. 
• Lesson 4-1, Vertical Alignment, Previous: Students recognized and represented proportional relationships between quantities. (7.RP.2) Now: Students graph and compare proportional relationships, interpreting the unit rate as the slope of the line. (8.EE.5)

The instructional materials for Reveal Math 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 and essential questions that are visibly shaped by CCSSM cluster headings. Examples include:

• In Module 2, the Goal, “Learn about the real number system by identifying, calculating, and estimating irrational numbers and comparing them to rational numbers.”, is shaped by 8.NS.A.
• In Module 6, the Essential Question, “How can systems of equations be helpful in solving everyday problems?”, is shaped by 8.EE.C.
• In Module 9, the Goal, “Analyze and use similar and congruent figures using transformations.”, is shaped by 8.G.A.

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. 

• In Lesson 4-3, 8.EE.B connects to 8.G.A as students connect similar triangles to slope. In Explore and Develop, Learn - Similar Triangles and Slope states, “How can you use slope triangles to find the slope of the line? Is the slope of the line the same, no matter which slope triangles are used? explain. Draw other slope triangles to support your explanation.” In Explore and Develop, Example 1 states, “The graph of the line t is shown. Use the similar slope triangles to compare the slope of segment AC and the slope of segment CE.”
• In Lesson 5-3, 8.F.B and 8.EE.B are connected as students write the y = mx+b equation to represent specific situations. Practice Question 2 states, “The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value. The write the equation of the function in the form y = mx + b.”
• In Lesson 7-1, 8.G.A connects to 8.EE.C as students write equations to find missing angle measures. Practice Question 10 states, “In the figure, line m is parallel to line n. If the measure of angle 3 = (7x - 10) degrees and the measure of angle 6 = (5x + 10) degrees, what are the measures of angle 3 and angle 6?”
• In Lesson 7-3, 8.G.B is connected with 8.EE.A as students use the Pythagorean Theorem to solve equations finding the missing side of a right triangle. Practice Question 3 states, “The diagonal of a television measures 27 inches. If the width is 22 inches, calculate its height to the nearest inch.”