## Reveal Math

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Reveal Math Course 3, Teacher Digital License, 1-year 9780078997679 Common Core Edition McGraw-Hill Education 2020
Reveal Math Course 2, Teacher Digital License, 1-year 9780078997648 McGraw-Hill Education 2020
Reveal Math Course 1, Teacher Digital License, 1-year 9780078997631 McGraw-Hill Education 2020
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### Overall Summary

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for alignment to the CCSSM. ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

​The instructional materials reviewed for Reveal Math Grade 8 meet expectations for not assessing topics before the grade level in which the topic should be introduced. 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.

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The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

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)

#### Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at approximately 82% of instructional time to the major work of the grade.

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Instructional material spends the majority of class time on the major cluster of each grade.

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.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the 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?”
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The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

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.
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Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

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”.

• 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)
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Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to 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.

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.”

### Rigor & Mathematical Practices

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

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Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons provide several opportunities that address conceptual understanding, and the materials include problems and questions that develop conceptual understanding throughout the grade-level.

• In the Teacher’s Edition, both Modules and Lessons begin with The Three Pillars of Rigor where conceptual understanding for the topic is briefly outlined. For example, Module 1, “In this module, students draw on their knowledge of exponents to develop understanding of the properties of exponents and scientific notation.”
• In Explore & Develop, Explore is “intended to build conceptual understanding through Interactive Presentations that introduce the concept and can be completed by pairs on devices or as a whole class through digital classroom projection.” For example, in Module 4, Lesson 4-1, Explore, “Students will be presented with a rate at which Marcus can download songs from the Internet. Throughout this activity, students will use a table, graph, and ratio to compare the number of minutes and the number of songs downloaded.” (8.EE.5)
• Some Checks address conceptual understanding. For example, Lesson 5-5 Check, "Determine whether the table represents a linear or nonlinear function. Explain." (8.F.3)
• Some Exit Tickets address conceptual understanding. Lesson 9-1 Exit Ticket, “What transformations can be used to show that triangle RST and triangle RST’ are congruent?” (8.G.2)

Examples of the materials providing opportunities for students to independently demonstrate conceptual understanding include:

• In Lesson 4-3, students develop conceptual understanding about the slope of a line being the same between any two points on the line. Explore - Right Triangles and Slope, “Inquiry question: How does the slope compare between any two pairs of points on a line? You will use Web Sketchpad to explore this problem.” Learn - Similar Triangles and Slope: “You can use the properties of similar triangles to show the ratios of the rise to the run for each triangle are equal.” Practice Question 5, “Multiselect. The graph shows similar slope triangles on a line. Select all of the statements that are true: The slope of the line is negative. The slopes of each triangle are the same because they lie on the same line. Triangle CDE has a greater slope because the triangle is larger. The slope of each triangle is 2/3. The slope of each line is positive.” (8.EE.6)
• In Lesson 5-2, students graph lines from function tables. This is extended in Lesson 5, Examples 1-3, when students identify linear and nonlinear functions from graphs and tables and, in Examples 3-5, functions from equations. (8.F.A)
• Lesson 6-1 Explore - Systems of equations: “Inquiry question: What does it mean when graphs of two linear equations intersect? You will use Web Sketchpad to explore this problem. Situation: Edna leaves a trailhead at dawn to hike toward a lake 12 miles away where her friend, Maria, has been camping. At the same time, Maria leaves the lake to hike toward the trailhead (on the same trail, but in the opposite direction). Edna is walking uphill, so her average speed is 1.5 miles per hour. Maria is walking downhill, so her average speed is 2 miles per hour. Select the Start/Stop Simulation button to see what happens on the hike. Select Reset to return the hikers to their starting points. Record your observations.” Students put the data into a table and a graph. “Talk about it!: What does the point of intersection represent?” (8.EE.8a)
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Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The structure of the lessons includes several opportunities to develop these skills. The instructional materials develop procedural skill and fluency throughout the grade-level.

• In the Teacher’s Edition, both Modules and Lessons begin with The Three Pillars of Rigor where procedural skill and fluency for the topic is briefly outlined. For example, Lesson 6-1, “In this lesson, students draw on their knowledge of graphing linear equations to build fluency with solving systems graphically.”
• Some Interactive Presentations (slide format) demonstrate procedures to solve problems. For example, in Lesson 1-3, Explore and Develop - Example 1: Problems include, “Simplify $$(8^6)^3$$” and “Simplify $$(k^7)^5$$.” Students are stepped through using the Power of a Power property. (8.EE.1)
• Some Checks address procedural skills and fluency. For example, Lesson 2-2 Check: “Solve $$y^2$$ = 256” (8.EE.2)

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level.

• Lesson 3-1: Students use properties of equality to solve equations with variables on each side algebraically. They have multiple opportunities in the lesson to practice procedures. Example 1: “Solve 3(8x+12) - 15x = 2(3 - 3x). Check your solution. Move through the steps to solve the equation.” The steps include: Write the equation; Distributive Property; Combine like terms; Addition property of Equality; Simplify; Subtraction property of Equality; Simplify; Division property of Equality; Simplify.” (8.EE.7)
• Lesson 6-3: Students solve systems of equations by substitution, rewrite equations to solve by substitution, and use procedures to solve systems with no solutions and infinitely many solutions. (8.EE.8)
• Lesson 10-3, Practice 1-4: “Find the volume of each sphere. Express your answer in terms of $$\pi$$. 2) Given illustration: a sphere with diameter 9 in.” (8.G.9)
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Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for Reveal Math Grade 8 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level.

• In the Teacher’s Edition, Modules and Lessons begin with The Three Pillars of Rigor where application for the topic is briefly outlined. For example, in Lesson 11-3, “In this lesson, students apply their understanding of writing linear equations to real-world problems by interpreting the slope and y-intercept of the line.”
• Each Module includes a Performance Task that addresses application. For example, in Module 6, Performance Task, “Keith and Margo are in the process of remodeling their home. The remodeling process consists of several projects. They will be adding new landscaping, pouring a new concrete patio, adding crown molding, and fixing their kitchen’s pantry. Some of the work they will do themselves, and for some of it, they will hire contractors. Part C. Keith and Margo are going to add crown molding around the perimeters of the ceilings of two rooms. The first room has dimensions and perimeter as shown below. The second room has the same length as the first room, a width that measures twice as much as the first room, and a perimeter, P, of 40 feet. Write a system of equations to represent this situation. Then solve the system of equations using the elimination method. State the dimensions of each room.”(8.EE.8)
• In Lesson 5-3, Reflect and Practice, Apply, Practice Question 2, “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 the initial value. Then write the equation of the function in the form y = mx + b.” (8.F.4)
• Some Checks address application. For example, in Lesson 4-5, Check, “Katie wants to attend fitness classes at a local gym. The cost of attending Fitness for Life is represented in the graph shown. Fitness World charges a registration fee of $90 plus$8 per month. Katie wants a membership for 18 months. Which gym charges less for 18 months? How much less?” (8.EE.6)

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts.

• In Lesson 3-2, Practice Questions, “Write and solve an equation for each exercise. Check your solution. 1) Marko has 45 comic books in his collection, and Tamara has 61 comic books. Marko buys 4 new comic books each month. After how many months will Marko and Tamara have the same number of comic books?” (8.EE.7)
• In Lesson 4-3, Practice Question 6, “Lines r and s are parallel, meaning they will never intersect. Draw similar slope triangles on each line and find the slope of each line. What conclusion can you draw about the slopes of parallel lines?” (8.EE.6)
• In Lesson 6-5, “A concession stand sells hot dogs and hamburgers. At the football game, 84 hot dogs and 36 hamburgers were sold for $276. At another football game, 18 hamburgers and 60 hot dogs were sold for$174. What is the cost of each hot dog and each hamburger?” (8.EE.8c)
• In Lesson 7-3, Apply, Maps, “Alma has a motor boat that averages 3 miles per gallon of gasoline, and the tank holds 15 gallons of gasoline. At 9 a.m., Alma left the dock. At 10 a.m., her position was 3 miles west and 4 miles north of the dock. If she continues at this rate, in how many more hours will the tank be out of gasoline?” (8.G.7)
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Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Reveal Math Grade 8 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Many of the lessons incorporate two aspects of rigor, with an emphasis on application, and practice problems for students to address all three aspects of rigor.

All three aspects of rigor are present independently throughout the materials, and examples include:

• In Lesson 9-1, Explore and Develop, Example 1, students develop understanding of transformations. Students determine if each pair of figures are congruent. If so, they describe a sequence of transformations that maps one figure onto the other figure. If not, they explain why they are not congruent. “Think About It!: How do you know that more than one transformation is needed to map ABC onto XYZ?” Students have an interactive eTool to move the triangles around the coordinate plane and record the sequence of their transformations. Finally, students “Talk About It!: Could you have first translated ABC 4 units up and then reflected it across the y-axis? Explain. Why is ABC congruent to XYZ?”. (8.G.2)
• In Lesson 5-2, Reflect and Practice, students develop understanding that a function is a rule that assigns to each input exactly one output. In the first three problems, given a function and the inputs, students complete the output column in a function table. At times, students generate both parts of the table such as Question 4: “A single-engine plane can travel up to 140 miles per hour. The total number of miles m is represented by the function m = 140h, where h is the number of hours traveled. Determine appropriate input values for this situation. Then complete the function table for m = 140.” (8.F.1)
• In Lesson 6-5, Practice Question 6, students use their understanding of simultaneous equations to find solutions to real-life situations. “At a farmer’s market, Amar purchased 4 jars of salsa and 3 cucumbers and spent a total of $12.25. Dylan purchased 1 jar of salsa and 2 cucumbers and spent a total of$4. Dakota purchased 1 jar of salsa and 5 cucumbers. If each jar of salsa costs the same and each cucumber costs the same, how much did Dakota spend?” (8.EE.8)

Examples of the materials integrating at least two aspects of rigor include:

• In Lesson 5-6, Practice Question 3, students use their understanding to sketch a graph that exhibits the qualitative features of a function that has been described verbally in real-world situations: “Ryan’s heart rate was steady before exercising. While exercising, his heart rate increased rapidly and then steadied. During cool down, his heart rate decreased slowly then lowered quickly until becoming steady again. Sketch a qualitative graph to represent the situation. Determine if the graph is linear or nonlinear and where the graph is increasing or decreasing.” (8.F.5)
• In Lesson 10-2, students develop understanding of the relationship between the volume of a cone and a cylinder by filling each with rice. Using conceptual understanding, students develop the volume formula and practice finding volume of various cones. Finally, they complete an application problem with a picture of a cone and a cylinder, both with 4 inch diameters and heights of 6 inches, “A family-owned movie theater offers popcorn in the sizes shown. Their cost for the popcorn is 0.09 per cubic inch. If each container is filled to the top, what is the difference between the costs of the popcorn in the two containers?” (8.G.9) #### Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice The instructional materials reviewed for Reveal Math Grade 8 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and clearly labeled throughout the materials, and the instructional materials support the standards’ emphasis on mathematical reasoning. ##### Indicator {{'2e' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for Reveal Math Grade 8 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level. All 8 MPs are clearly identified throughout the materials, including: • The materials contain a Correlation to the Mathematical Practices PDF which includes explanations and descriptions of the MPs and examples of MPs located in specific lessons. • Within the digital module opener and lesson, the Standards tab contains a list of the MPs found in that specific module/lesson. The same list is part of the Teacher Edition PDF. Throughout each lesson, the program indicates each opportunity for students to engage in the practices, with an MP symbol and a description of how to connect the MP to the content within the lesson. • In Reflect and Practice, questions intended to engage students in the MPs are specifically noted with an MP symbol. The Teacher Edition states which of the MPs each practice question is intended to align with. • Performance Task rubrics list which MPs students are intended to engage in during the task. • Each component of the digital materials (Learn, Explore, Examples, Apply) contains an About this Resource narrative explaining how related MPs should specifically be addressed within the activity. The same information is found in the Teacher Edition PDF in the margin labeled MP Teaching the Mathematical Practices. • Each lesson includes Launch - Today’s Standards: How can I use these Practices? The Teacher’s Notes recommend that teachers, “Tell students that they will be addressing these content and practice standards in this lesson. You may wish to have a student volunteer read aloud How Can I meet this standard? and How can I use these practices? and connect these to the standards.” Examples of the MPs being used to enrich the mathematical content include: • MP1: In Lesson 10-4, Explore and Develop, Apply, Shopping, students make sense of the problem to determine using the formula for the volume of cylinders when solving real-world problems. “A local grocery store sells corn in two different-sized cans. A one-meter wide shelf is being stocked. How many more of the smaller cans will fit on the shelf than the larger cans?” • MP2: In Lesson 6-2, Explore and Develop, Example 3, students demonstrate reasoning with the prompt, “Talk About It! Describe a method you can use to verify the system has infinitely many solutions.” • MP8: In Lesson 4-2, Explore and Develop, Explore, Slope of Horizontal and Vertical Lines, students use regularity and repeated reasoning to enhance their understanding of slope. “This Explore spans eight slides. Working in pairs, students will be presented with a series of lines whose slopes approach zero or infinity. Throughout this activity, students will view the patterns of slopes as they approach zero or infinity and make conjectures as to the slopes of all vertical and horizontal lines.” There are instances where the labeling of MPs is inconsistent, and examples of this include: • In Lesson 4-1, Example 3 is labeled with MPs 3 and 5 in the digital materials, but in the print materials, the same problem is not labeled with any MPs. ##### Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed for Reveal Math Grade 8 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MP5, and examples include: • The materials identify the tool(s) students use. For example, in Lesson 5-2, “Students will use the Coordinate Graphing eTool to graph the function in the coordinate plane.” In Lesson 7-1, “Students will use Web Sketchpad to explore the relationships between angles created by parallel lines and transversals.” In Lesson 11-1: “Students will use the Coordinate Graphing eTool to generate a scatter plot.” • In the Teacher’s Edition, teachers are occasionally prompted to encourage students to compare tools, but students do not choose the tools. For example, in Lesson 5-1, MP5 is identified, “Use Appropriate Tools Strategically. Students will use Web Sketchpad to explore and model the real-world relationship between input and output values. Encourage students to use the tools of this Explore (input-output-ordered pair table and mapping diagram) to explain how a mapping diagram can help them understand the relationship between input and output.” Examples of the materials attending to the full meaning of MPs include: • MP1: In Lesson 4-5, Explore and Develop, Apply, “Amir wants to ship a birthday present to his brother. Express Shipping charges a5 insurance fee to protect items that are shipped and $0.50 for every ounce the item weighs. Priority Postal’s shipping costs are shown in the graph. The present Amir wants to ship weighs 14.2 ounces. Which company charges less to ship the present? How much less?” The graph for Priority Postal shows cost ($) vs Weight (oz) and does not show 14.2 oz (the weight of the present).
• MP2: In Lesson 1-2, Explore and Develop, Learn, “When simplifying a quotient of powers using the Quotient of Powers Property, why do the bases have to be the same? For example, why can’t you use the Quotient of Powers Property to simplify $$x^8/y^3$$?” Also in Lesson 7-3, Explore and Develop, Example 3, “Find the missing leg length. A plane takes off from an airport and travels 13 miles on its path. If the plane is 12 miles from its takeoff point horizontally, what is its height?”
• MP4: Students create situations such as in Lesson 6-5, Practice Question 8, “Create. Write a real world problem that can be solved using a system of equations.Then solve the problem.” or in Lesson 11-1, Practice Question 7, “Create. Describe a situation that the scatter plot shown might represent. Then interpret the scatter plot.” Also, in Apply problems, teachers are prompted, “Instead of instructing students on a particular strategy, encourage them to use their own strategies to solve the problem and to evaluate their progress along the way. They may or may not find that they need to change direction or try out several strategies.”
• MP7: In Lesson 6-4, Practice Question 14, “Describe the structure of a system of equations for which it is more efficient to solve using elimination rather than substitution.” or in Lesson 9-4, Explore and Develop, Example 1, “Determine whether rectangle HUKL is similar to rectangle MNPQ. If so, write a similarity statement. The students determine the structure of two figures if corresponding angle measures are congruent and corresponding side lengths are proportional.”
• MP8: In Lesson 1-2, Practice Question 14, “Consider the sequence below: 2, 4, 8, 16, 32, 64 … The number 4,096 belongs to this sequence. What is the number that immediately precedes it?” Also, in Lesson 2-2, Practice Question 16, “Reasoning. Simplify each expression. Then write a rule for the pattern. a. $$(\sqrt81)^2$$ b. $$(\sqrt9/16)^2$$ c. $$(\sqrt0.04)^2$$ d. $$(\sqrt t)2$$."
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Reveal Math Grade 8 meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples of the materials prompting students to both construct viable arguments and analyze the arguments of others include:

• Talk About It! in lesson examples are often opportunities for students to create viable arguments. For example, in Lesson 9-4, “Can you assume that the two rectangles are similar just because their corresponding angles are congruent? Explain.”
• In Lesson 1-3, Practice Question 13, “Make an argument for why $$(4^2)^4 = (4^4)^2$$.”
• In Lesson 8-1, Practice Question 12, “Reason Inductively. Determine whether the following statement is always, sometimes, or never true. Write an argument that can be used to defend your solution: A preimage and its translated image are the same size and the same shape.”
• Write About It! within lesson examples are often opportunities for students to engage with MP3. In Apply of many lessons, students are prompted to “Write About It! Write an argument that can be used to defend your solution.”
• In Lesson 4-4, Practice Question 10, “Find the Error. The cost of apps varies directly with the number of apps purchased. Aditi bought four apps for a total of \$5.16. She found the direct variation equation below for this relationship. Find her mistake and correct it.”
• In Lesson 5-2, Practice Question 10, “Justify Conclusions. Liam’s truck has a 25 gallon tank and uses 0.05 gallon of gas for every mile driven. When creating a table for the function y = -0.05x + 25, Liam argues that he can only use positive rational numbers for the input. Is Liam correct? Justify your answer.”
• In Lesson 8-1, Practice Question 11, “A classmate states that a two-dimensional figure could have each of its vertices translated in different ways and it would still be considered a translation. Explain to your classmate why this is incorrect.”
##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Reveal Math Grade 8 meet the expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking.

• In Resources, there is a Correlation to the Mathematical Practices, Grade 8, which defines the Standards for Mathematical Practice. For example, MP3 is defined, there are examples connected to MP3, and states, “Students are required to justify their reasoning and to find the errors in another’s reasoning or work. Look for the Apply problems and the exercises labeled as Make a Conjecture, Find the Error, Use a Counterexample, Make an Argument, or Justify Conclusions. Many Talk About It! question prompts ask students to justify conclusions and/or critique another student’s reasoning. In the Teacher Edition, look for the Teaching the Mathematical Practices tips labeled as this mathematical practice.”
• There are Questions for Mathematical Discourse in Develop and Explore of each lesson. For example, in Lesson 11-3, Extra Example 2, the teacher notes suggest, “Use these questions for mathematical discourse, “Why are choices A and C incorrect?; How different would your conjecture be for a 65 year old?”.
• Talk About It! is designed to elicit student justification. For example, in Lesson 6-3: “As students discuss the Talk About It! question (In Step 2 you substituted -1 for x into the equation y = 3x + 8. You can also substitute -1 for x into the other equation 8x + 4y = 12. Why is either method correct? Which do you prefer? Explain.), encourage them to create a plausible argument to defend why either method is correct, and why they prefer their chosen method.”
• The materials also prompt teachers to have students share their responses to Write about it!. Teacher guidance throughout the materials states, “As students respond to the Write About It! prompt, have them make sure their argument uses correct mathematical reasoning. If you choose to have them share their responses with others, encourage the listeners to ask clarifying questions to verify that the reasoning is correct.” The Write About It! prompts typically read, “Write an argument that can be used to defend your solution.”
• The Teacher Edition includes Teaching the Mathematical Practices tips which involve developing arguments. For example, in Lesson 8-3, Learn, “While discussing the Talk About It! question on Slide 2, encourage students to create a plausible argument and draw a counterexample to illustrate why these coordinate notations are only valid for rotations about the origin.”
• Teacher’s Notes often give prompts and suggestions for facilitating arguments. For example, in Lesson 5-1, Practice Question 8, the teacher notes state, “In Exercise 8, students will explain why the relationship is a function. Encourage students to identify the information that identifies the relationship as a function.”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Reveal Math Grade 8 meet the expectations for explicitly attending to the specialized language of mathematics.

The materials use precise and accurate mathematical terminology and definitions, and the materials support students in using them. Teacher’s guides, student books, and supplemental materials explicitly attend to the specialized language of mathematics.

• In Resources, there is a Correlation to the Mathematical Practices, Grade 8, which defines the Standards for Mathematical Practice. For example, MP6 is defined, there are examples where MP6 can be found, and states, “Students are routinely required to communicate precisely to partners, the teacher, or the entire class by using precise definitions and mathematical vocabulary. Look for the exercises labeled as Be Precise. Many Talk About It! prompts ask students to clearly and precisely explain their reasoning. In the Teacher Edition, look for the Teaching the Mathematical Practices tips labeled as this mathematical practice.”
• In each Module introduction, What Vocabulary Will You Learn? prompts teachers to lead students through a specific routine to learn the vocabulary of the unit.
• Many Lessons have a “Language Objective.” For example, in Lesson 7-1, “Students will state and apply the definition of angle relationships formed by parallel lines cut by a transversal: exterior angles, interior angles, alternate exterior angles.”
• In each lesson, Math Background briefly describes key concepts/vocabulary or directs teachers to an online component to learn background. Definitions are not included, but are accessible in the glossary. Glossary definitions are precise and accurate, and there are definitions for math content and math models. In addition, the glossary references the lesson where the vocabulary is introduced.
• The lesson Launch includes a vocabulary section that introduces new vocabulary for the lesson. During Develop and Explore, the new vocabulary is always bolded and defined. For example, in Lesson 4-5, Learn: “The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.”
• In Lesson 5-1, What Vocabulary Will You Learn?, Teacher questions include: “What does the prefix co- mean? What is the everyday meaning of the word constant? What part of speech is the word like in like terms? How does it help you understand what like terms might be?”
• When students see vocabulary in successive lessons, What Vocabulary Will You Use? assists teachers in facilitating discussions that help students apply the vocabulary they have previously learned.
• In Lesson 3-3, Teaching Notes for Interactive Slideshows state, “When discussing the Talk About It! question on Slide 2 (How can you make sure that you solved the equation correctly?), encourage students to use clear and precise mathematical language, such as substitute  or replace, when describing how they can check to verify they solved the equation correctly.”
• In Lesson 1-2, Example 3, the teacher notes prompt, “Encourage students to use academic vocabulary, such as Product of Powers Property to explain how to simplify the expression.”
• Each Module includes a Vocabulary Test. “This summative assessment asset is designed for students to demonstrate their knowledge, understanding, and proficiency of the vocabulary covered in this module.”

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

##### Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials for Reveal Math Grade 8 meet the expectations that there is a clear distinction between problems and exercises in the materials.

In the instructional sections of each lesson, students complete examples and problems to learn new concepts through strategies such as guided instruction, step-by-step procedures, interactive slideshows, and problem solving.

Each lesson ends with independent practice, which include exercises that allow students to independently apply what they have learned. Some of the practice problems parallel the examples presented in the lesson, while others are labeled as Higher-Order Thinking Problems or Test Prep.

##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for Reveal Math Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

Modules include a Launch, which provides students an overview of the topics found in the module. A Vertical Alignment tab provides teachers information on Vertical Alignment between and within grade levels. Lessons are presented in a logical order that builds coherence throughout the grade.

Each Lesson follows a consistent format that develops learning through building conceptual understanding, providing opportunity for practice of procedural skills, and providing application in real-world situations. Exercises intentionally encourage a progression of understanding and skills, and the format includes three main sections, each including multiple parts:

• Launch: Warm Up (addresses prerequisite skills); Launch the Lesson (includes class discussions and short videos; Today’s Standards; and What Vocabulary Will You Learn?.
• Explore and Develop: Explore (provides Inquiry questions for the students to explore); Learn (guided instruction); Examples (scaffolded problems for students to work through); Apply (guided application problems); and Check (one problem follows each example to assess student understanding).
• Reflect and Practice: Exit Ticket; Practice Problems; Spiral Review Lesson; and Assessments (when applicable).
##### Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials for Reveal Math Grade 8 meet the expectations for prompting students to show their mathematical thinking in a variety of  ways. Examples include:

• In Lesson 1-4, students use a table to explain expressions with negative and zero exponents.
• In Module 3, students use manipulatives (algebra tiles and a balance), in student pairs, to write and solve multi-step algebraic equations.
• In Lesson 4-5, students model and compare multiple representations - table, graph, equation, situation - of data when writing linear equations.
• In Lesson 5-3, students verbally defend or critique the work of others in written form to show understanding when constructing linear functions.
• In Lesson 6-1, students use online tools to graph (graphing etool).
• In Lesson 7-4, students construct and solve equations to find missing angle measures in triangles.
• In Module 8, students use Web Sketchpad to explore and model transformations on the coordinate plane.
• In Module 1, Performance Task, students evaluate data in a table, order the asteroids, and compute distance, mass, and volume using the given position, radius, and mass related to the situation.
• In all lessons, students use a digital platform to conduct and present their work.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials for Reveal Math Grade 6 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives, although the materials rarely include physical manipulatives.

• Manipulatives and other mathematical representations are consistently aligned to the mathematical content in the standards.
• Virtual manipulatives, such as number lines, double number lines, bar diagrams, pie charts, algebra tiles, x-y tables, coordinate planes, and flashcards, are used for developing conceptual understanding.
• There are embedded links to programs such as Web Sketchpad and eTools.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for Reveal Math Grade 8 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

The page layout in the materials is consistent, user-friendly, clearly labeled, and not overcrowded or hard to read. The graphics within both the Student book and Online Interactive material are colorful, engaging, and represent items that are relevant. Each section of the Lesson is found in separate documents, making it easy to navigate, though only a limited amount of information can be viewed on each page. Student practice problem pages are available in digital, download, and print form and include enough space for students to write their answers and provide explanations.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for Reveal Math Grade 8 partially meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons. It does not include explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing teachers with quality questions for students. These questions support teachers in planning and providing effective learning experiences.

• Questions are consistently provided throughout each lesson to help guide students’ mathematical development. The questions develop vocabulary of the  lesson, encourage mathematical discourse, develop conceptual understanding, promote justifications of thinking, and include differentiated questions to ask while students engage in the Interactive Presentation. Examples include: “If the triangles are similar, what do you know about the lengths of the sides?” and “What does it mean if your answer is not a whole number?”
• The Teacher Edition provides question prompts that are additional to what is in the student materials.
• Explore sections include Inquiry Questions such as, “Why is writing an equation a useful way to represent and solve a real world problem?”
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials for Reveal Math Grade 8 meet the expectations for containing annotations and suggestions on presenting the content and using embedded technology for student learning.

The Teacher’s Edition contains annotations and suggestions in the margin notes at every phase of instruction, including students’ independent practice. In addition, teachers are provided with ample planning information at the Module and Lesson levels.

Annotations and suggestions at the Module level include:

• Module Goal
• Be Sure to Cover (prerequisites required)
• Coherence (vertical alignment)
• Rigor (how rigor is specifically addressed in the module)
• Suggested Pacing
• Analyze the Probe (what the probe measures, targeted misconceptions, when to assign the probe, actions that should be taken after the probe)
• Essential Questions (suggestions for students’ graphic organizers)
• What Will You Learn? (students self ratings before and after)
• Dinah Zike Foldables (instructions for foldables)
• Launch the Module (notes on what the Launch video addresses)
• Pause and Reflect
• What Vocabulary Will You Learn?
• Are You Ready? (prerequisite information)
• Mindset Matters (notes on risk taking, regular reflection, “Not Yet” Doesn’t Mean “Never”, etc.)

Annotations and suggestions at the Lesson level include:

• Content standards and Mathematical Practices
• Essential Question
• Lesson Activities
• Differentiate (including Resources and Language Development Support)
• Vertical Alignment (containing Previous, Now, and Next learning)
• Rigor
• Mathematical Background
• What if my students don’t have devices?

Cues to reference online resources include:

• Videos on how to teach the Mathematical Practices
• Assistance with the Talk About It! questions to promote discourse
• Performance reports of the checks
• Extra examples
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials for Reveal Math Grade 8 partially meet the expectations for containing adult-level explanations so teachers can improve their own knowledge of the subject.

There are a limited number of “The Why Behind the Math” videos for teachers “that dive into math concepts. Dr. Nevels explores the “what” and “why” behind the math, addresses misconceptions, and gives strategies you can use to help students understand math more deeply.” These provide insight for teachers and could also be used with students. Videos may be added as there are “coming soon” flags.

In each lesson, Mathematical Background addresses the mathematical content of the lesson, but the descriptions are primarily procedures and definitions rather than designed to improve teacher knowledge, for example:

• In Lesson 5-2, “A function table is a table that displays input and outputs pairs for a function. Function tables can be created from function rules by substituting appropriate input values into the rule to find the corresponding output values. The graph of the function is the set of ordered pairs generated from the function rule. A linear function is a function whose graph is a straight line. Linear functions have equations of the form y = mx + b.”
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials for Reveal Math Grade 8 do not meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Vertical alignment is provided, but does not explain the role of the grade-level mathematics in the context of the overall mathematics curriculum for grades K-12. Previous, Now, and Next include connections within the grade level or to the grade levels immediately before and after the current grade.
• The publisher intends to address this with a resource that is “Coming Soon in 2019”: Content Progressions Resources - “This library contains resources that show the progression of math concepts for elementary through high school math.” Cathy Seeley will discuss what to expect in each course and point out critical areas students will learn. She will “give insight into the progression of math concepts from previous grades to the current grade and beyond.”
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials for Reveal Math Grade 8 provide a list of lessons, cross referencing standards, and a pacing guide. Recommended Pacing is provided and includes instructional times for each lesson and module. Major work standards are identified, and a correlations document, found in the front matter of the Teacher’s Edition and in the online resources, shows which standards are addressed in each lesson. Within each online module, there is a tab for pacing and standards addressed.

##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials for Reveal Math Grade 8 include strategies for parents to support their student’s progress. In each Module, the Launch includes a family letter written in English. Family letters can be added to the student pages, included in the Launch presentation, emailed, or sent home with students. The letter explains what students have previously learned, what they will learn in the current module, vocabulary that will be used, and how parents can provide support including suggested activities for home that might be helpful to support students in the content of the module. There is also an invitation to contact the teacher if more information is needed. The parent letter can be read aloud in the docReader.

##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials for Reveal Math Grade 8 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

In the Teacher Edition, the Guiding Principles of Reveal are based on current mathematics education research: Rigor, Productive struggle, Formative assessment, Rich tasks, Mathematical discourse, and Collaborative learning.

The expert advisors are listed with a short note from each about instruction that aligns with current research. These include sense-making in mathematics, students discussing their thinking and the thinking of others, supporting students with technology as they construct mathematical understanding, sparking student curiosity, promoting productive struggle, creating enjoyable mathematical experiences for students, and using formative assessment to elicit student misconceptions and addressing them through instruction.

In the online resources, teachers are provided with a short video by Cathy Seeley that discusses the teacher’s role using the Reveal program and how the program aligns with current research in mathematics education.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials reviewed for Reveal Math Grade 8 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge and strategies for teachers to identify and address common student errors and misconceptions. The assessments do not clearly denote which standards are being emphasized.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. There are multiple opportunities to gather information about prior knowledge and prepare for the content addressed in the Module.

In the beginning of the school year, Diagnostic and Placement Tests can be assigned to determine whether a student has mastered prerequisite concepts for the current course.

At the beginning of each Module, Be Sure to Cover lists prerequisite skills required for the module. The Module Pretest can be used to diagnose student readiness for the module, and Are You Ready? has a few exercises over necessary prerequisite concepts. The Teacher Edition contains an extensive list of prerequisite concepts.

At the beginning of each Lesson, Warm-Up exercises address prerequisite skills for the lesson.

##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• Formative Assessment Math Probes by Cheryl Tobey provide an analysis of targeted misconceptions. “This formative assessment asset helps the teacher to target common misconceptions students may have about the mathematics covered in this module. The Teacher’s Guide provides a key as well as a description of common misconceptions, and how they might be addressed.” There is one per Module which can be completed more than once to ensure that misconceptions have been addressed.
• Each lesson notes anticipated misconceptions, and teachers are provided ideas to help students address them.
• Within Independent Practice, there are Common Misconception pointers related to specific problems such as, “Students may mistakenly order integers based on absolute value rather than numerical value or vice versa.” and “Some students may not identify like terms correctly when one of the coefficients is 1 or -1 since the number 1 is not written explicitly.”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• After each example in a lesson, there is a Check to assess understanding of that component of the lesson. These are done online so teachers can access performance reports. If students do not “pass”, teachers can assign relevant practice.
• Exit Tickets are provided in every lesson.
• Put It All Together, mid-module, formative assessments provide opportunities to assess student understanding of multiple lessons.
• Classroom discourse has students discuss their thinking and provides another formative assessment opportunity for teachers to identify what students have learned and respond with appropriate prompts and clarifications.
• Test Practice pages are provided at the end of each module to help students review module content and prepare for online assessments. Many of the exercises mirror the questions students will see on the online assessments.
• Each lesson contains additional digital practice allowing students to complete several problems, getting immediate feedback about what is correct.
• Some lessons include a digital Spiral Review containing content from multiple lessons. The resource notes specify the exact concepts on the Spiral Review.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials for Reveal Math Grade 8 do not meet the expectations for assessments clearly denoting which standards are being emphasized.

• Summative assessments are available online; however, standards are not linked to the online assessments or specific items. Standards for the overall Module are identified; assessments align to the Module lessons.
• Performance Tasks Rubrics provide a list of standards correlations for the assessment as a whole but not for individual questions. Performance Tasks are optional (not built into the suggested pacing guide), so they may not be utilized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for Reveal Math Grade 8 partially meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• In the Checks, completed after each Example in the lessons, teachers can reference the performance results and are guided to assign differentiated practice as needed for remediation.
• A chart is provided for teachers on the End of Module Review pages. Related standards and lessons for each question are referenced and can be used to determine areas of strength/weakness.
• Summative assessments are available and scored online. No answer keys or suggestions for follow-up are available.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for Reveal Math Grade 8 provide opportunities for students to monitor their progress.

• At the beginning of each Module, students are provided with a Before and After chart that lists each topic of the lesson. Students place a check in three separate columns: don’t know, have heard of it, or know it!. At the end of the Module, students revisit this chart in Rate Yourself to determine how their understanding has grown.
• At the end of each Module, students provide a written response to prompts such as explaining one thing they have learned and one question they still have about the module content.
• Reflect on the Module has students answer the Essential Question of the Module, often by completing a graphic organizer.
• Within each lesson, Pause and Reflect provides prompts for students to consider their learning such as, “Did you ask questions about today’s lesson? Why or why not?” “Where in the lesson did you feel the most confident? Why?” “Are you ready to move on to the Example? If yes, what have you learned that you think will help you? If no, what questions do you still have? How can you get those questions answered?”

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials reviewed for Reveal Math Grade 8 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations and include extension activities for advanced students, but do not present advanced students with opportunities for problem solving and investigation of mathematics at a deeper level. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each module introductory page includes Be Sure to Cover which identifies prerequisite skills students need for the module content.
• Each module and lesson includes tabs for pacing and vertical alignment. Vertical Alignment makes connections to both prior and future knowledge and skills to assist with sequencing instruction.
• The Warm Up at the beginning of each lesson “helps the teacher determine whether students are proficient in the prerequisite skills needed for this lesson.”
• Each Module includes a Pretest that can be used to “diagnose students' understanding of the prerequisite skills required for this module.”
• Teachers Notes are embedded alongside the lessons and student tasks that provide prompts that scaffold instruction.
• Discussion questions are embedded in the Examples and Apply tasks.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• The opening page to each lesson contains Differentiate that lists learning resources available for use. These are identified and color-coded in the Teacher Edition as Approaching Level (AL), On Level (OL), and Beyond Level (BL). They include collaboration strategies, Remediation and Extension Tasks, and Arrive Math which is an intervention program integrated into Reveal Math.
• Questions for Mathematical Discourse in the Teacher Edition margin are also identified and color-coded as AL, OL, or BL.
• After each problem during the instruction portion of the lesson, there is a computer-based Check to gauge student understanding. The Teacher’s Guide provides direction on using the data to assign practice problems and other exercises.
• Each lesson has Additional Examples that help students reinforce their understanding of the concept. It includes an extra problem for the teacher to use, as well as questions to help elicit meaningful responses.
• Supporting All Learners, an online resource, includes a Language Development Handbook which provides graphic organizers, note taking using sentence frames, and vocabulary worksheets.
• Digital Differentiate activities include auto-scored Lesson Practice problems, Collaboration Strategy activities related to the math concepts/vocabulary, prerequisite skill Review activities, and a Personal Tutor.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for Reveal Math Grade 8 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Talk About It! and Write About It! prompts often encourage students to describe their approaches to problems and to think about other possible approaches.
• Each lesson presents an Inquiry question for students to explore, often with a digital resource such as Web Sketchpad.
• Apply tasks include a variety of entry-points and a variety of solution strategies.
• Common prompts for Apply problems involve different approaches to the tasks or strategies that students could use.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials for Reveal Math Grade 8 meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations.

In the Teacher’s Edition, ELL icons introduce various supports specifically related to students’ native languages such as a Spanish Interactive Student Edition, Digital Spanish Personal Tutors, or a Multilingual eGlossary. Additional supports for ELLs and other special populations include:

• Math-Language Building Activities
• Language Scaffolds
• Think About It! and Talk About It! prompts that assist in deepening understanding
• Audio options
• Graphic organizers
• A Language Development handbook found online in Program Resources.
• Language Objectives for almost every lesson
• What Vocabulary Will You Learn? at the beginning of each lesson. The Teacher Edition provides a prompt for ELL students: “As you proceed through the chapter, introduce each vocabulary term using the following routine. Ask the students to say each term aloud after you say it. Define...Example…Ask…”
• Each module has a Foldable Study Organizer containing key concepts/vocabulary which students create.

The Arrive Math Booster is a Tier 2 intervention program which provides digital mini-lessons for students who need a different presentation of the content addressed in the lesson.

##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for Reveal Math Grade 8 partially meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. There are multiple attempts to address the needs of advanced learners, but they do not always provide students with opportunities to explore or experience enrichment in their learning.

Extensions are included but often do not present students with opportunities for problem solving and investigation of mathematics at a deeper level. Tasks are guided or modeled rather than students investigating on their own.

For example, Extension, Mixture Problems in an interactive slideshow, Lesson 3-4:

• Slide 1 presents a situation requiring a mixture and provides a completed table to organize the information.
• Slide 2 shows how to write an equation from the data in the table.
• Slide 3 shows and explains the steps for isolating a variable in one equation then substituting into the other equation.
• Slides 4 and 5 are additional situations, showing the same steps to reach a solution.
• Slides 6-9 are four practice problems for students that have drop-down, fill-in-the blank frameworks for solving.

Other activities provide more opportunities for students to investigate and discover such as:

• Enrichment Activity: “To further students’ understanding of the Pythagorean Theorem, have them work with a partner to use the internet or another source to research Pythagorean Triples. Have them generate several examples of Pythagorean triples, and work to make a conjecture as to how many Pythagorean Triples there are in which length of the hypotenuse is under 100 units. They should be to justify their conjectures. Have them present their findings to the class.”

Differentiated teacher prompts also address levels of learners, including Beyond Level (BL), which attempts to investigate concepts at a greater depth such as:

• Beyond Learning: “How much faster would the Japanese train need to travel per hour in order to travel the same distance per hour as the Chinese train?” (comparing functions)
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for Reveal Math Grade 8 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Multinational names are used in the examples and practice. Cartoon characters presented in the textbook represent students of both genders and various ethnicities.
• The diversity of names throughout the problems are used in ways that do not stereotype characters by gender, race, or ethnicity.
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways not expressing gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
• When people are shown, there is a balance of demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials for Reveal Math Grade 8 provide opportunities for teachers to use a variety of grouping strategies. Throughout the lessons, the materials use an identifiable symbol for whole groups, small groups, and individual instruction. These icons are posted at the top of the teacher’s edition pages and within the materials. Pairs/Small Groups is a common structure to allow students to process and explain verbally.

##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials for Reveal Math Grade 8 encourage teachers to draw upon home language and culture to facilitate learning.

• The student glossary is printed in both English and Spanish.
• Personal tutor videos are in both English and Spanish.
• Interactive Student Edition eBook, Spanish Sampler - currently available for only one Module at each grade.
• Each Module includes a Family Letter in English that describes the program and resources that are available to students.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials reviewed for Reveal Math Grade 8: integrate technology in ways that engage students in the mathematics; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials for Reveal Math Grade 8 are web-based and compatible with multiple internet browsers. The teacher resources and student books are platform neutral and can be accessed on mobile devices.

##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials for Reveal Math Grade 8 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

• Check and Apply problems within the lessons are designed to be completed and scored online.
• Each lesson has an optional Practice set of content questions designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Some lessons have a Spiral Review designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Each module has one or two Put It All Together reviews over multiple lessons which can be completed and scored online, with instant feedback for responses as correct or incorrect.
• Each module has a Formative Assessment Probe that can be completed via technology, but not auto-scored.
• All module and benchmark assessments are designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Assessments can be created using various item banks organized by module, practice, or test questions. Questions contain tech-enhanced capabilities and can be edited and saved in the My Questions folder.
• The Reveal Math Reporting Dashboard provides data on completed assignments and assessments. An Item Analysis Report and a Standards report are available for a specific class or individual students.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials for Reveal Math Grade 8 include opportunities for teachers to personalize learning for all students.

• Teachers have the option to assign approaching level, on-level, or beyond level practice problems and assessments.
• Teachers can select and assign individual practice items for student remediation based on the Check formative assessment data.
• Teachers can create and assign classes online.
• Arrive Math Booster Mini-lessons and LearnSmart are often referenced in the materials as options to provide more support; however, currently, there is nothing available to review.

The instructional materials for Reveal Math Grade 8 are not easily customized for local use.

• The materials provide differentiated intervention, but Modules and Lesson components are sequenced in a particular order for students to develop understanding and complete the independent practice.
• There is some flexibility in presentation because teachers can “pick and choose” how many examples to use based on the needs of their students or allow independence in working through the interactive slideshows rather than providing guidance.
• Teachers can create and upload files, attach links, and attach docs which can be assigned to students.
• Teachers can create assessments using a bank of items or using self-written questions and assign to students.
• There are additional Examples and Apply problems that could be assigned as needed.
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

The instructional materials for Reveal Math Grade 8 do not provide opportunities for teachers to collaborate with other teachers or students to collaborate with other students via technology.

##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The instructional materials for Reveal Math Grade 8 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software.

• Each module begins with Launch, a video about the topics in the Module and how they are applied in real world.
• Personal Tutor videos are in Review and Assess for students to watch independently if they need examples explained.
• There are interactive tools and virtual manipulatives such as Web Sketchpad, eTools, Desmos, Virtual Manipulatives, flashcards, etc. Students are routinely directed to the tools, but they are not able to access these tools on their own.
• Interactive slideshows and assessments allow students to use features such as drag and drop, multi-select, swipe, type, and expand features.
• Interactive slideshows encourage students to watch videos and animations within the presentations, reviewing prerequisite concepts and seeing mathematical processes for current skills. Note-taking and problem-solving are included in presentations.

## Report Overview

### Summary of Alignment & Usability for Reveal Math | Math

#### Math 6-8

The instructional materials reviewed for Reveal Math Grades 6-8 meet expectations for alignment to the Common Core State Standards for Mathematics and meet expectations for usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

###### Alignment
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###### Usability
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