## Reveal Math Integrated

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

Title ISBN Edition Publisher Year
Reveal Math Integrated I Student Digital License, 1-year Subscription 9780077007027 McGraaw-Hill Education 2020
Reveal Math Integrated II Student Digital License, 1-year Subscription 9780077007119 McGraaw-Hill Education 2020
Reveal Math Integrated III Student Digital License, 1-year Subscription 9780077007621 McGraaw-Hill Education 2020
Reveal Math Integrated I Teacher Digital License, 1-year Subscription 9780077007720 McGraaw-Hill Education 2020
Reveal Math Integrated II Teacher Digital License, 1-year Subscription 9780077007812 McGraaw-Hill Education 2020
Reveal Math Integrated III Teacher Digital License, 1-year Subscription 9780077007911 McGraaw-Hill Education 2020
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## Report for High School

### Overall Summary

The instructional materials reviewed for Reveal Math Integrated meet the expectations for alignment to the CCSSM for high school, Gateways 1 and 2. In Gateway 1, the instructional materials meet the expectations for focus and coherence, and the instructional materials show strengths in attending to the full intent of the mathematical content contained in the high school standards, spending the majority of time on the CCSSM widely applicable as prerequisites, letting students fully learn each non-plus standard, engaging students in mathematics at a level of sophistication appropriate to high school, and explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. In Gateway 2, the instructional materials meet the expectation for reflecting the balances in the Standards and helping students meet the Standards' rigorous expectations by giving appropriate attention to procedural skills, conceptual understanding, and applications. Also in Gateway 2, the instructional materials meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

##### High School
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus & Coherence

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).

The instructional materials reviewed for Reveal Math Integrated meet expectations for focus and coherence. The materials attend to the full intent of the mathematical content contained in the high school standards, spend the majority of time on the CCSSM widely applicable as prerequisites, let students fully learn each non-plus standard, engage students in mathematics at a level of sophistication appropriate to high school, and explicitly identify and build on knowledge from Grades 6-8. The materials partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards and making meaningful connections in a single course and throughout the series.

##### Indicator {{'1a' | indicatorName}}
The materials focus on the high school standards.*
##### Indicator {{'1a.i' | indicatorName}}
The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The instructional materials reviewed for Reveal Math Integrated meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students.

Examples of the materials attending to the full intent of the standards include:

• N-RN.1: In Integrated Math II, Module 10: Exponents and Roots, Lesson 4, students explore nth roots through a number line activity to show the values of raising a number to the ½ power. In the print materials, students explain their reasoning for why different expressions with rational exponents and roots are equivalent.
• A-CED.1: In Integrated Math II, Module 9: Linear Equations, Inequalities, and Systems, Lesson 1, students create and solve equations and inequalities in one variable algebraically and graphically.
• A-APR.3: In Integrated Math III, Module 2: Polynomials and Polynomial Functions, Lesson 4, students find the zeros of a polynomial using synthetic division and then sketch the graph. In Integrated Math III, Module 3: Polynomial Equations, Lesson 5, Example 5, students analyze a real life example to find zeros and then also graph the function.
• F-BF.2: In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lesson 5; Module 8: Exponential Functions, Lessons 5 and 6; and Module 9, Lessons 5 and 6, students write both arithmetic and geometric sequences recursively and with an explicit formula.
• G-CO.1: In Integrated Math I, Module 10: Tools of Geometry, Lesson 2, the materials provide precise definitions in “Today’s Vocabulary” for concepts and provide questions that link the vocabulary with the mathematics students complete that day.
• G-GPE.5: In Integrated Math I, Module 12: Logical Arguments and Line Relationships, Lesson 8, the materials establish the relationship between slopes of parallel and perpendicular lines. In the “Watch Out” section, students extend this relationship to the slopes of vertical and horizontal lines. Students use these relationships to compare different forms of linear equations.
• S-IC.1: In Integrated Math III, Module 8: Inferential Statistics, Lesson 1, the materials provide a video lesson that highlights the different types of sampling. This provides students with clear examples to understand how to make inferences based on different types of samples.

The following standards are partially addressed in the materials:

• A-SSE.1a: Students and teachers do not interpret parts of expressions. Students often create expressions, but they do not interpret what parts of a given expression mean.
• G-CO.2: Students and teachers do not compare transformations that preserve distance and angle measures to those that do not.
• G-GPE.1: Students and teachers do not complete the square in the context of the equation of a circle.

The following standards are not addressed in the materials:

• F-LE.3
• G-SRT.1a
##### Indicator {{'1a.ii' | indicatorName}}
The materials attend to the full intent of the modeling process when applied to the modeling standards.

The instructional materials reviewed for Reveal Math Integrated partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. Throughout the series, all aspects of the modeling process are present in isolation or in combination with other aspects, but there are no instances where students engage in the full modeling process without prompts or scaffolding from the materials.

Examples where students engage in some, or all, aspects of the modeling process with prompts or scaffolding from the materials include, but are not limited to:

• In Integrated Math I, Module 6: Relations and Functions, Lesson 6, students collect data about wrist and neck circumferences of their classmates and examine the data on a graph. From this data, students interpret if the function is either a linear or non-linear relationship and if the function is applicable to the real world (F-IF.5). Students do not define their variables in this scenario.
• In Integrated Math I, Module 7: Systems of Linear Equations and Inequalities, Performance Task: Work, Save, Travel, students determine how many hours Rue will work at two different jobs while trying to save money for a trip. The performance task has nine prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
• In Integrated Math II, Module 12: Quadratic Functions, “Ignite! Mathematical Modeling,” students use a set of data to predict the price of a movie ticket in 2027. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
• In Integrated Math II, Module 3: Similarity Performance Task, students determine the results on the design and materials needed for a t-shirt based on different dilations being performed on the original figure in the design. The performance task has four prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
• In Integrated Math II, Module 6: Measurement, “Ignite! Mathematical Modeling,” students design an aquarium that will support a certain number of two types of fish based on given parameters for the dimensions of the aquarium and information about what each type of fish needs to survive. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
• In Integrated Math II, Module 9: Linear Equations, Inequalities, and Systems, Performance Task, students determine how to optimize Steven’s income from his business that specializes in computer application training and data entry support services using linear programming techniques. The performance task has six prompts that move students through different aspects of the modeling process, but students do not complete the modeling process on their own.
• In Integrated Math III, Module 6: Inverses and Radical Functions, “Ignite! Mathematical Modeling,” students use a set of data to predict when the winning time for solving a Rubik’s Cube will be less than 3 seconds. Students answer seven prompts that proceed through the aspects of the modeling process, and the prompts are scaffolded by the aspects of the modeling process. After the seven prompts are answered, students report their findings and more prompts are divided to help students provide a complete report.
• In Integrated Math III, Module 8: Inferential Statistics, Introduction, students interpret and report their findings. The materials provide some questions for students to ask themselves when doing a modeling problem, such as “What do you notice? What questions can you ask? What assumptions are you making?” However, these questions are not utilized with other modeling problems. Students pose questions about two different spinners and begin to formulate strategies for solving the questions they come up with about the spinners. Students do not define variables or compute the numerical answers to the questions they formulate (S-IC.1).
##### Indicator {{'1b' | indicatorName}}
The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
##### Indicator {{'1b.i' | indicatorName}}
The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

The instructional materials reviewed for Reveal Math Integrated meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers. The instructional materials spend a majority of the time on the WAPs, and the amount of time spent on the WAPs decreases across the courses of the series.

Examples of how the materials spend the majority of time on the WAPs include:

• In Integrated Math I, Module 3: Relations and Functions, students represent functions in multiple ways, analyze graphs, and give the domain and range of graphs (F-IF). Throughout the first six lessons, students determine if given relations are functions, identify key features of functions, and determine the relationships between the different representations of the functions.
• In Integrated Math II, Module 10: Exponents and Roots, Lessons 4-6, students simplify expressions using the properties of exponents (N-RN.1) and apply those to operations with radical expressions. These lessons provide multiple opportunities for students to practice.
• In Integrated Math II, the materials develop the relationships within and between similar triangles throughout Module 3: Similarity, (G-SRT.B).
• In Integrated Math II, Module 9: Linear Equations, Inequalities, and Systems, Lesson 1, students write equations and inequalities that represent real world situations and solve them algebraically and by graphing (A-CED.1,2).
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 1, students practice graphing quadratic equations using tables and rate of change (F-IF).
• In Integrated Math III, Module 4: Inverse and Radical Functions, Lesson 3, students explore what radical expressions have numeric solutions and which do not. They think particularly about what happens when the expression will have a real solution or not when the radicand has a negative value (A-SSE).
##### Indicator {{'1b.ii' | indicatorName}}
The materials, when used as designed, allow students to fully learn each standard.

The instructional materials reviewed for Reveal Math Integrated, when used as designed, meet expectations for letting students fully learn each non-plus standard. Overall, students would fully learn most of the non-plus standards when using the materials as designed.

The non-plus standards that would not be fully learned by students across the series include:

• A-SSE.4: Students do not derive the formula for the sum of a finite geometric series.
• F-TF.5: Students do not choose what trigonometric function to use as the trigonometric function is provided within the context of the problem.
• G-CO.8: Students examine triangle congruence, but they do not explain the criteria for triangle congruence on their own.
• G-SRT.1b: In Integrated Math II, Module 3: Similarity, Lesson 1, students complete one problem to verify the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
• S-CP.7: Students use the addition rule and find probabilities of events in Integrated Math II, Module 7: Probability, Lesson 6. However, students do not interpret their answers in terms of the model.
##### Indicator {{'1c' | indicatorName}}
The materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The instructional materials reviewed for Reveal Math Integrated meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age-appropriate contexts, apply key takeaways from Grades 6-8, and vary the types of real numbers being used.

Examples of the materials using age-appropriate contexts include:

• In Integrated Math I, Module 7, students solve systems of equations in contexts that  include: selling plastic and wood frames, buying new clothes, buying school supplies, working with drones, building computers, and a kayak travelling on a stream.
• In Integrated Math II, Module 12: Quadratic Functions, Lesson 1, Extra Example 6, students interpret the graph of a jumping skateboarder.
• In Integrated Math I, Module 10: Tools of Geometry Assessment, students create their own game on a basketball court (Module Test Form C, Problem 23A) and analyze different things about an animal shelter and a grooming service (Test Practice  Problem 13).
• In Integrated Math II, Module 5: Circles, Lesson 1, students find the circumference of a traffic circle (Example 3) and a carousel (Extra Example 3).
• In Integrated Math II, Module 9: Linear Equations, Inequalities and Systems, Lesson 5 Practice: Form A Problem 12, students write a system of equations that relates the difference between one-on-one and team games played in basketball.
• In Integrated Math III, Module 2: Polynomials and Polynomial Functions, Assessments, students choose a polynomial function that models profit for a business.
• In Integrated Math III, Module 7: Rational Functions, Lesson 6, students solve rational equations to  determine the number of tickets needed to cover the cost of prom.

Examples of applying the key takeaways from Grades 6-8 include:

• In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lesson 2, students apply their understanding of slope and rate of change (8.EE.5b) to solve real-world problems. Students apply this understanding in Integrated Math I, Module 4, Lesson 4, to transformations of linear functions (F-BF.3) and in Integrated Math I, Module 5: Creating Linear Equations, Lesson 3, to lines of best fit (S-ID.6a).
• In Integrated Math I, Module 12: Logical Arguments and Linear Relationships, students use relationships between lines and angles (8.G.5) to prove segment and angle relationships in Lessons 5 and 6, (G-CO.9).
• In Integrated Math II, Module 3, Lesson 6, students use triangle proportionality to solve problems and prove theorems (7.RP.2).
• In Integrated Math II, Module 4, lesson 3, students used the Pythagorean Theorem and its converse to solve problems (8.G.5).
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 3, students add and subtract complex numbers by combining like terms (8.EE.7b) and using the commutative property of addition (6.EE.3).

The materials vary the types of real numbers being used. Within the Learn sections, the majority of numbers used are integers. Within the practice sections and assessments, there are more non-integer problems and solutions. Examples of this include:

• In Integrated Math I, Module 2, Lesson 6, the materials provide a variety of solution types for the proportional solutions. Most of the solutions are whole numbers, but there are a variety of decimal and integer solutions throughout the lesson.
• In Integrated Math I, Module 11: Angles and Geometric Figures, the assessment has decimal solutions to problems for surface area and volume problems in various contexts.
• In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lesson 4, students use both rational and irrational numbers to find the missing side lengths of right triangles.
• In Integrated Math II, Module 12: Quadratic Functions, Lesson 6, students solve many types of quadratic equations that have whole number, rational, and irrational solutions.
• In Integrated Math III, Module 5: Polynomial Equations, Lesson 5, students find integer, irrational, and imaginary roots of polynomial functions.
##### Indicator {{'1d' | indicatorName}}
The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

The instructional materials reviewed for Reveal Math Integrated partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Lessons within units and individual courses build upon and connect to each other. However, the materials do not make several connections across the courses.

Within each course, “Coherence” indicates what students have learned previously, what they are currently learning, and what they will learn next. Examples of these connections within courses include:

• In Integrated Math I, Module 14: Triangles and Congruence, Lesson 1, students solve problems using the triangle sum and exterior angle theorems (G-CO.10), which is connected to the previous learning of transformations and symmetries in Integrated Math I, Module 13: Transformations and Symmetry, Lesson 6 (G-CO.3). The materials extend this to the future learning of proving triangles congruent in Integrated Math I, Module 14: Triangles and Congruence, Lesson 2, (G-SRT.5).
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 2, students solve equations by graphing and relate the solutions to the zeros of the function (A-CED.1), and in Lesson 7, students connect the graphs of quadratics to solve quadratic inequalities. In Integrated Math III, Module 3: Polynomial Equations, Lesson 1, students connect the zeros of the function to solve the polynomial equations. In Integrated Math III, Module 6: Logarithmic Functions, students use the zero product property to solve logarithmic functions (A.CED-1).

Examples of connections that are not made across courses include, but are not limited to:

• In Integrated Math I, Module 2: Equations in One Variable, students use proportional relationships to solve real-world problems. In Integrated Math II, Module 3: Similarity, Lessons 5 and 6, students use proportions in triangle relationships, and in Integrated Math III, Module 7: Rational Functions, Lesson 6, students use proportions in solving rational equations. There are no connections made for either the teacher or students as to how these lessons are connected.
• In Integrated Math II, Module 4: Right Triangles and Trigonometry, students examine trigonometric ratios in right triangles. Integrated Math III, Module 9: Trigonometric Functions, students encounter trigonometric functions and the unit circle. There is no connection made between trigonometric ratios from Integrated Math II and how they can be used to understand and extend to the unit circle and trigonometric functions.
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 3, students have imaginary numbers as solutions to quadratic equations. The lesson states, “In your math studies so far, you have worked with real numbers. However, some equations, such as $$x^2 + x + 1 = 0$$ do not have real solutions.” There is not a connection for teachers or students to content from previous courses.
##### Indicator {{'1e' | indicatorName}}
The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The instructional materials reviewed for Reveal Math Integrated meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the high school Standards.

The instructional materials build on knowledge from Grades 6-8, and they explicitly identify standards from Grades 6-8 in the teacher materials throughout the series. Standards from Grades 6-8 are explicitly identified for many lessons in Vertical Alignment, and each module indicates prerequisite skills with “Are you Ready?” which includes a bulleted list of skills not explicitly related to standards from Grades 6-8.

The following are examples of where the materials build on and explicitly identify standards from Grades 6-8:

• In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lesson 2, “Conceptual Bridge,” students “expand their understanding of and fluency with linear functions (first studied in Grade 8) to graphing linear functions by using a table and by using intercepts. They apply their understanding of slope and rate of change by solving real-world problems” (8.EE.5,6).
• In Integrated Math II, Module 10: Exponents and Roots, Lesson 4, students extend their understanding of the properties of integer exponents (8.EE.1) as they encounter rational exponents.
• In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lesson 5, students solve problems using trigonometric ratios (G-SRT.6), which builds on their understanding of ratios (6.RP, 7.RP), similarity (8.G.4), and right triangles (8.G.B).
• In Integrated Math III, Module 4: Inverses and Radical Functions, Lesson 4, students use their understanding of square roots and cube roots from Grade 8 (8.EE.2) to graph and solve radical equations (F-IF.7b).
##### Indicator {{'1f' | indicatorName}}
The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

The instructional materials reviewed for Reveal Math Integrated are inconsistent in explicitly identifying the plus standards and using the plus standards to coherently support the mathematics which all students should study in order to be college and career ready.

In the correlation document that exists for each course, “CCSS for Mathematics correlated to Reveal”, the plus standards are identified at times, but in the lessons in the teacher edition, the plus standards are not identified. However, the standards are aligned to a traditional sequence of courses instead of an integrated series, and there was not a document for Integrated Math I. Due to this inconsistency, teachers may not be able to determine whether a lesson or standard could be omitted.

The following are examples where the plus standards coherently support the non-plus standards:

• N-CN.8-9: In Integrated Math III, Module 1: Quadratic Functions, Lesson 6, students extend their understanding of roots of quadratic equations to solve problems with imaginary roots. Students also connect the value of the discriminant of a quadratic equation to the graph of the quadratic equation.
• F-TF.6: In Integrated Math III, Module 9: Trigonometric Functions, Lesson 7, students restrict a trigonometric function to identify different properties of the function.
• G-SRT.9-11: In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lessons 6-8, students use non-right triangles to derive the formula for the area of a triangle and the Laws of Sines and Cosines. Students solve real-world problems using the three formulas.
• G-C.4: In Integrated Math II, Module 5: Circles, Lesson 5, students use either geometry software or a compass and straightedge to construct tangent lines to a circle. This is an application of the constructions completed in class and provides another opportunity for students to practice and make sense of their constructions. Students make connections between radii, tangents, and circumscribed angles during the activity.
• S-CP.8,9: In Integrated Math II, Module 7: Probability, Lessons 4 and 5, students solve problems using permutations and combinations, reflect on their work in writing, and interpret their answers in terms of the model.
• S-MD.6,7: In Integrated Math II, Module 7: Probability, Lesson 3, students use probability to make fair decisions about areas and explore simulations and conduct experiments to make sense of given statistical models, which extends the work with probability from previous modules and lessons.
• A-APR.5: In Integrated Math III, Module 2: Polynomials and Polynomial Functions, Lesson 5, the materials present the Binomial Theorem. Students answered two questions using the Binomial Theorem, but this work using probability was not connected to the rest of the content of the lesson.

Evidence for the following plus standards was not found in the materials:

• N-CN.3-6
• N-VM
• A-APR.7
• A-REI.8-9
• F-IF.7d
• F-BF.1c
• F-BF.4b-5
• F-TF.3,4,9
• G-GPE.3
• G-GMD.2
• S-MD.1-5

### Rigor & Mathematical Practices

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: The instructional materials reflect the balances in the Standards and help 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 reviewed for Reveal Math Integrated meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Overall, all three elements of rigor are thoroughly attended to and interwoven in a way that focuses on the needs of a specific standard as well as balancing procedural skills, application, and conceptual understanding.

##### Indicator {{'2a' | indicatorName}}
Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Reveal Math Integrated meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The digital materials have exploration activities and applets to aid in the development of conceptual understanding, and they provide opportunities for students to demonstrate that understanding throughout the series.

Examples of where the materials develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding include, but are not limited to:

• In Integrated Math II, Module 12: Quadratic Functions, Lesson 4, students relate the factors of an equation to the solutions of a quadratic equation (A-APR.B), and in Integrated Math III, Module 3: Polynomial Equations, Lesson 5, “Explore,” students determine how the value of the discriminant impacts the type and number of zeros of a quadratic function. In “Learn,” students examine examples of the relationship between zeros, roots, and factors and demonstrate their conceptual understanding of the concept introduced in “Explore.”
• In Integrated Math I, Module 2: Equations in One Variable, Lessons 2-4, students solve equations using the algebraic properties of equality (A-REI.1). Students use algebra tiles to develop their conceptual understanding and provide algebraic justifications for their steps in solving equations. In “Learn,” students provide the steps and properties justifying the steps when solving equations to demonstrate their understanding of solving equations.
• In Integrated Math I, Module 4: Linear and Nonlinear functions, Lesson 1, students determine what it means for a point to be a solution to an algebraic equation (A-REI.10). “Math Background” states, “The coordinates of the points on the line are the solutions of the related linear equation.” The materials assess this idea within the “Inquiry” question, “How is the graph of a linear equation related to its solution?” In Integrated Math III, Module 6: Logarithmic Functions, Lesson 1, students solve logarithmic equations and make the connection between the solutions of logarithmic functions and the points of intersection on the graphs of the function.
• InIntegrated Math I, Module 3: Relations and Functions, Lesson 2, students determine whether relations are functions (F-IF.A). In “Launch the Lesson,” students examine a website of 6.3 million selfies to determine if the relationship between the independent and dependent variables represents a function. Students demonstrate their understanding of what a function is and determine whether relations are functions in mappings, tables, graphs, etc.
• In Integrated Math II, Module 4: Right Triangle and Trigonometry, Lesson 1, students use similarity in right triangles to develop proportional relationships within right triangles (G-SRT.6). In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lesson 5, students complete an interactive activity which establishes the ratios between pairs of side lengths based on given angle measures.
• In Integrated Math I, Module 5: Creating Linear Equations, Lesson 1, students make a generalization about how changing coordinates of points changes the slope of an equation. Within the lesson, students interpret the slope and y-intercept of an equation (S-ID.7), and in Integrated Math I, Module 4: Linear and Nonlinear functions, students interpret rates of change in real-world relationships.

An example of the materials not developing conceptual understanding and providing opportunities for students to independently demonstrate conceptual understanding is:

• In Integrated Math II, Module 10, Lesson 4, the materials include steps for writing equivalent expressions with rational exponents using the exponent of ½ as an example (N-RN.1). The materials do not develop a connection between integer and rational exponents, and in “Explore”, practice problems, students do not independently demonstrate their understanding of this standard.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Reveal Math Integrated meet expectations for providing intentional opportunities for students to develop procedural skills, especially when called for in specific content standards or clusters. Often, these procedural skills occur across multiple modules with varied practice.

Examples of how the materials develop procedural skills across the series include, but are not limited to:

• A-SSE.2: In Integrated Math I, Module 1: Expressions, Lesson 4, students rewrite expressions using the distributive property and by factoring the greatest common factor out of an expression. In Integrated Math II, Module 11: Polynomials, Lessons 4-7, students multiply and factor special products, and in Integrated Math III, Module 3: Polynomial Equations, Lessons 2 and 3, students learn more factoring techniques and use polynomial identities to rewrite expressions that are not easily factorable otherwise.
• A-APR.1: In Integrated Math II, Module 11: Polynomials, Lessons 1-3, students practice the operations of addition, subtraction, and multiplication with polynomials. These skills are also developed in Integrated Math III, Module 2: Polynomials and Polynomial Functions, Lesson 3, along with showing closure under these operations. Through these lessons, students have multiple opportunities to practice operations with polynomials.
• F-BF.3: In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lessons 4 and 7, students examine transformations of linear and absolute value functions respectively. Transformations of functions are also developed in Integrated Math III, Module 4: Inverse and Radical Functions; Integrated Math III, Module 5: Exponential Functions; and Integrated Math III, Module 7: Rational Functions. In all cases, students use embedded technology to explore how the parameters change the graph of a function and identify and justify the effects of changing certain parameters.

Examples of how the instructional materials provide opportunities for students to independently demonstrate procedural skills include, but are not limited to:

• A-APR.6: In Integrated Math III, Module 2: Polynomials and Polynomial Functions, Lesson 4, students use long division and synthetic division to rewrite rational expressions, and there are many examples for students to practice each type of division.
• G-SRT.5: Within the Geometry course, there are many opportunities for students to justify congruence and similarity criteria for triangles. In Integrated Math I, Module 14: Triangles and Congruence, Lessons 3 and 4, students use triangle congruence to solve problems. In Integrated Math II, Module 3: Similarity, Lessons 3 and 4, students demonstrate skill with triangle similarity by solving problems and demonstrate that two triangles are similar using the similarity criteria.
• G-GPE.5: In Integrated Math I, Module 5: Creating Linear Equations, Lesson 2, students write equations of parallel and perpendicular lines through a given point. In Integrated Math I, Module 12: Logical Arguments and Line Relationships, Lesson 8, students justify the slope criteria for parallel and perpendicular lines and demonstrate finding parallel or perpendicular lines through a given point.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Reveal Math Integrated meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. The materials utilize different contexts across the series, such as population modeling, maximum profit, expenditures for a party, zip-lining, and numerous sports applications. Throughout the series, students apply conceptual understandings and procedural skills that have been developed.

Examples of applications across the series include, but are not limited to:

• A-REI.11: In Integrated Math I, Module 7: Systems of Linear Equations and Inequalities, Lesson 1, students predict the approximate year when the populations of China and India will be the same by approximating the average rate of change of both populations, writing a system of equations to represent the situation, and graphing the system to determine their solution. Students work in teams or small groups to contextualize and make sense of the problem.
• G-SRT.8: In Integrated Math II, Module 4: Right Triangle and Trigonometry, Lessons 2 and 6, students use angles of elevation and trigonometry to solve problems in different outdoor settings. In Lesson 2, students find the length of a zipline given different measurements of length and angle measure, and in Lesson 6, students use trigonometric ratios to determine how far a drone is from a given location.
• S-IC.1: In Integrated Math III, Module 8: Inferential Statistics, Lesson 2, Examples 3 and 4, students determine if a raffle is fair or unfair. Students create and run a model or simulation of the raffle to determine fairness.
##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.

The instructional materials reviewed for Reveal Math Integrated meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Throughout the materials, students engage in each of the aspects of rigor. All three aspects of rigor are present independently throughout the materials, and there are instances where multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding.

Examples of where the instructional materials attend to conceptual understanding, procedural skills, and application independently throughout the grade level include, but are not limited to:

• Conceptual understanding is developed in the digital materials through “Launch the Lesson” in which students consider how the content relates to real-life scenarios. For example, in Integrated Math III, Module 9: Trigonometric Functions, Lesson 2, students find the heights of clouds using trigonometry and using a clinometer as a mathematical tool.
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 4, students apply factoring quadratic functions. Students “find how long it takes a car to accelerate given the distance and rate travelled” by factoring a quadratic equation, determining the zeros of the quadratic function, and interpreting when the car will be at the maximum acceleration.
• In some “Learn” sections, students develop procedural skills. For example, in Integrated Math I, Module 7: Systems of Linear Equations and Inequalities, Lesson 2, students find intersection points on a graph to find a solution. The materials demonstrate how substitution relates to finding intersection points, and students complete multiple practice problems to develop the procedural skill for themselves.

Examples of where two or more of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding include, but are not limited to:

• In Integrated Math I, Module 5: Creating Linear Equations, Lesson 1, students use the web sketchpad to explore how changing points on a line impacts the slope of the line. Students practice procedural skills by writing equations in slope-intercept form given a slope and a point or two points. Students apply their understanding to create a linear equation that models the number of students enrolled in high schools in the U.S. since 2010. Students also interpret the y-intercept and slope in the context of the problem once they have created the equation.
• In Integrated Math II, Module 2: Quadrilaterals, Lesson 4, students write equations of four lines in the coordinate plane to form a rectangle. Students demonstrate their understanding of the definition of a rectangle. Students also determine how two lines can be perpendicular or parallel, find the distance of line segments, and find points of intersection for the equations of lines.
• In Integrated Math III, Module 2: Polynomials and Polynomial Functions, “Ignite,” students solve a problem involving a bridge by answering the questions, “What do you notice?” and “What can you ask?” Students create a question about the scenario and develop a strategy to solve the question about the bridge. There are extensions in the materials for students to compare different spans for the bridge that would allow more practice with the procedure.

#### 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 Integrated meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials support the intentional development of overarching, mathematical practices, reasoning and explaining, and seeing structure and generalizing. The materials also support the development of modeling, but they do not consistently support the intentional development of choosing and using appropriate tools.

##### Indicator {{'2e' | indicatorName}}
The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Reveal Math Integrated meet expectations for supporting the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards.

Examples of MP1 include, but are not limited to:

• In Integrated Math I, Module 10: Tools of Geometry, Lesson 4, “Think About It,” students answer, “Why do you think the Distance Formula uses absolute value?” Students make sense of the idea that line segments cannot have negative values for their lengths.
• In Integrated Math I, Module 14: Triangles and Congruence, Lesson 1, “Teaching the Mathematical Practices” states, “In Example 1, guide students through the use of the 4-step plan to identify the meaning of the problem and look for entry points to its solution.” The materials provide explicit instructions for how to make sense of a mathematical problem.
• In Integrated II, Module 1: Relationships in Triangles, Lesson 3, “Apply,” the materials take students through a four step process to analyze the task. In each step, students ask themselves the following questions, “What is the task?”; “How will you approach the task? What have you learned that you can use to help you complete the task?”, “What is your solution?”; and “How can you know that your solution is reasonable?”
• In Integrated Math III, Module 7: Rational Functions, Lesson 2, teachers encourage students to transform expressions in both the numerator and the denominator to help them make sense of the expression.

Examples of MP6 include, but are not limited to:

• In Integrated Math I, Module 5: Creating Linear Equations, Lesson 5, the materials define the linear regression correlation coefficient and explain its meaning. Students attend to precision when explaining the graph, paying specific attention to labels and units in the problem.
• In Integrated Math II, Module 7: Probability, Lesson 4, “Communicate Precisely” states, “Encourage students to routinely write or explain their solution methods. Point out that they should use clear definitions when they discuss their solutions with others.” This occurs in multiple modules and lessons throughout the series.
• In Integrated Math III, Module 9: Trigonometric Functions, Lesson 2, students calculate with precision to determine the trigonometric ratios for an angle whose terminal side passes through a given point.
##### Indicator {{'2f' | indicatorName}}
The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Reveal Math Integrated meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards.

Examples of MP2 include, but are not limited to:

• In Integrated Math I, Module 6: Linear Inequalities, Lesson 2, students model multi-step inequalities with algebra tiles and consider their representation of the inequality algebraically. Students answer the question, “How can you model and solve a multi-step inequality?” to reason abstractly about the process.
• In Integrated Math I, Module 12: Logical Arguments and Line Relationships, Lesson 9, using the relationships between pairs of angles formed when two parallel lines are cut by a transversal, students write an equation that abstractly represents the relationship between the angle measures for a pair of angles and solves the equation to find the missing angle measures.
• In Integrated Math II, Module 2: Quadrilaterals, Lesson 4, students recognize the basketball court as a parallelogram and use the fact that a parallelogram has bisecting diagonals to solve the problem. The “Think About It” question brings the student back to the intersection of the diagonals and asks them to discuss what it represents.
• In Integrated Math III, Module 5: Exponential Functions, Lesson 2, “Teaching the Mathematical Practices” states, “Encourage students to consider how they could write a system of equations to represent the relationships among the number of visitors that visited the three parks.” Throughout the lesson, students write systems of equations that represent relationships between quantities in real-world scenarios, and in Problem 26, students explain how to recognize a system with infinitely many solutions.

Examples of MP3 include, but are not limited to:

• In Integrated Math I, Module 3: Relations and Functions, Lesson 3, “Think About It,” students construct an argument about if it is possible for a function to be discrete and continuous at the same time.
• In Integrated Math I, Module 11: Angles and Geometric Figures, Lesson 2, students construct arguments and communicate them to others. In Example 1, students answer the following question, “Adrian claims that if two complementary angles are both acute, then a pair of supplementary angles must both be obtuse. Do you agree? Explain why or why not.”
• In Integrated Math I, Module 14: Triangles and Congruence, Lesson 1, students use dynamic geometry software to make conjectures about the interior angles of triangles. Through their exploration, students construct an argument for the triangle angle sum theorem.
• In Integrated Math II, Module 5: Circles, Lesson 2, Example 3, students use stated assumptions, definitions, and previously stated results to construct an argument to determine the measurement of an arc from a circle graph.
• In Integrated Math III, Module 4: Inverse and Radical Functions, Lesson 6, students solve an equation that includes an extraneous solution. Students critique their own reasoning by answering the question, “In the example above, could you tell that four was an extraneous solution before checking the result? Explain your reasoning.”
##### Indicator {{'2g' | indicatorName}}
The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Reveal Math Integrated partially meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. The series encourages students to use a variety of tools, but there are not moments where students make a choice about which tool is most appropriate to use.

Examples of MP4 include, but are not limited to:

• In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lesson 3, students write an equation that represents the number of job openings after a given amount of time based on given information about how many jobs are open in the month of May and how job availability has increased per month since May. Students apply their understanding of slope and initial value to determine the equation of the line and to answer specific questions about the situation.
• In Integrated Math I, Module 10: Tools of Geometry, Lesson 3, students find the distance from a house to a coffee shop by applying the idea of betweenness to calculate the distance. Students draw a diagram, define variables, and write an equation to model the problem before solving.
• In Integrated Math II, Module 4: Right Triangle and Trigonometry, Lesson 5, students find the height of a cell phone tower. After giving students the information for the problem, the materials pose the question, “Which trig ratio would you use and justify your choice?”, and students also answer, “What would you have done differently if you had to find the length of the guide wire?”
• In Integrated Math III, Module 7: Rational Functions, Lesson 6, students solve for the number of hours it will take a second fuel line to fill a tanker and explain the solution. Students write a function, use the graph to find approximate solutions, and interpret their solutions in the context of the problem.

Examples of students using a variety of tools but not choosing which tools to use include, but are not limited to:

• In Integrated Math I, Module 4: Linear and Nonlinear Functions, Lesson 7, students use dynamic geometry software to graph absolute value functions and transformations of them. The geometry software occurs in the digital materials, and in the print materials, students are directed to use tables of values and graphs to visualize the transformations.
• In Integrated I, Module 10: Tools of Geometry, Lesson 3, students make constructions with a compass and straightedge, dynamic geometry software, and a reflective device. A teacher’s note states to “make a variety of tools available. Model tools effectively, including their benefits and limitations. Encourage the use of multiple tools for communication, calculation, investigation, and sense making.” However, students are directed which tools to use as they solve problems in the materials.
• In Integrated Math II, Module 1: Relationships in Triangles, Lesson 1, students locate the center of a circle that passes through the vertices of a triangle. In the lesson, students are directed to use a ruler, protractor, and compass to determine the center.
• In Integrated Math III, Module 5: Exponential Functions, Lesson 1, students are directed to use a graphing calculator to find a specific year in which a population will exceed 150.
##### Indicator {{'2h' | indicatorName}}
The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Reveal Math Integrated meet expectations for supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. In the materials, students find and use patterns and generalize findings from regularity in repeated reasoning. Within the print materials, there are Higher Order Thinking problems that provide students with opportunities to describe patterns and make connections from their repeated reasoning.

Examples of MP 7 include, but are not limited to:

• In Integrated Math I, Module 8: Exponential Functions, Lesson 6, “Explore and Develop,” students use the structure of a geometric sequence to write a recursive formula for the sequence. In Integrated Math III, Module 5: Exponential Functions, Lesson 4, students use the structure of geometric sequences to convert between recursive and explicit forms of the sequences.
• In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lesson 5, students explore the structure of right triangles to discover trigonometric ratios. Students complete an inquiry process that ends with the question, “If two right triangles have the same angle measure, what do you know about the trigonometric ratios of the angle?”
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 6, students use the discriminant to make connections between different values of the discriminant and the number and types of roots of the quadratic equation.

Examples of MP 8 include, but are not limited to:

• In Integrated Math I, Module 7: Systems of Linear Equations and Inequalities, Lesson 1, students examine the slopes and y-intercepts of equations in a system for patterns to determine the number of solutions of the system.
• In Integrated Math II, Module 10: Equations and Roots, Lesson 1, students explore provided examples to look for a pattern to determine the product of two expressions with exponents. In “Explore,” students express regularity in repeated reasoning to write the general product of two expressions with exponents.
• In Integrated Math III, Module 3: Polynomial Functions, Lesson 3, students find patterns in expanding and simplifying polynomial expressions to provide justification for polynomial identities.

### 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 Integrated 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 reviewed for Reveal Math Integrated meet expectations in 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 Reflect and Practice, which includes exercises that allow students to independently apply what they have learned. Practice exercises are found in the exit ticket, practice, spiral review, and activities.

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

The instructional materials reviewed for Reveal Math Integrated meet 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 courses. Lessons are presented in a logical order that builds coherence throughout the course.

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 how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.

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

• In Integrated Math I, Module 2: Expressions, Introduction, students create a foldable to organize their notes.
• In Integrated Math I, Module 13: Transformations and Symmetry, Lesson 1, students use dynamic geometric software to explore reflections by manipulating coordinates.
• In Integrated Math II, Module 10: Equations and Roots, Lesson 2, students fill in the blanks to answer missing steps of problems and construct responses to answer Think About It! Questions.
• In Integrated Math II, Module 4: Right Triangles and Trigonometry, Lesson 5, students match trigonometric ratios to trigonometric expressions.
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 1, students use an interactive sketch to explore quadratic functions in the coordinate plane.
• In Integrated Math III, Module 8: Inferential Statistics, Lesson 4, students construct a relative frequency table and graph the probability distribution.
##### Indicator {{'3d' | indicatorName}}
Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Reveal Math Integrated 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 LearnSmart, Desmos, Web Sketchpad, ALEKS, and eTools.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials reviewed for Reveal Math Integrated 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 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.

#### 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 Integrated 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, and a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons. The materials do 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 reviewed for Reveal Math Integrated meet 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.
• The Teacher Edition provides question prompts that are additional to what is in the student materials.
• Explore sections include Inquiry Questions such as “How is graphing a linear inequality on the coordinate plane similar to and different from graphing on the number line?” (Integrated Math I, Module 6: Linear Equations, Lesson 5)
##### 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 reviewed for Reveal Math Integrated meet expectations for containing annotations and suggestions on presenting the content and using embedded technology for student learning.

The Teacher 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 that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials reviewed for Reveal Math Integrated partially meet 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. These videos are not correlated to the integrated sequence, but could be used as supplemental materials if they were correlated to the series.

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 Integrated Math I, Module 14: Triangles and Congruence, Lesson 4, “The Angle-Side-Angle Postulate, written as ASA, and the Angle-Angle-Side, or AAS, Theorem can also be used to prove triangle congruence.”
• In Integrated Math II, Module 11: Polynomials, “A polynomial times a monomial is multiplied by applying the Distributive Property. The monomial is multiplied times each term in the polynomial. Any constant factors are multiplied times each other, while like variable bases are multiplied times each other, increasing the degree of the monomial.”
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 4, “Quadratic equations can be solved using several different methods. Factoring can be a quick method. Once a polynomial has been factored, the Zero Product Property may be used to find the roots of the equation. If the polynomial is difficult to factor or is not factorable, then other methods must be used.”
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.

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

Vertical alignment is provided, but does not explain the role of grade-level mathematics in the context of the overall mathematics curriculum for grades K-12. Previous, Now, and Next include connections within the course or to the courses before and after the current course.

##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials reviewed for Reveal Math Integrated 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. Standards are identified, and a correlation document, found in the front matter of the Teacher 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 students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials reviewed for Reveal Math Integrated provide one Family Letter per course. The Family Letter is located in the Program Overview: Welcome to Reveal Math, under Get Started. The letter includes an introduction to the program and suggestions for how parents can support their students.

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

The instructional materials reviewed for Reveal Math Integrated 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 Integrated meet 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, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, assessments that clearly denote which standards are being emphasized, and rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

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

The instructional materials reviewed for Reveal Math Integrated meet 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.

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 support for teachers to identify and address common student errors and misconceptions.

The instructional materials reviewed for Reveal Math Integrated meet 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 titled “Watch Out!” related to specific problems such as, “When determining the quantity to multiply by when rationalizing the denominator, make sure you raise the entire term under the radical to the power of n-x.” (Integrated Math III, Module 4: Inverse and Radical Functions, Lesson 5)
##### Indicator {{'3o' | indicatorName}}
Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

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

• Check questions accompany one or more examples to assess student understanding. 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 assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for Reveal Math Integrated meet expectations for assessments clearly denoting which standards are being emphasized.

Teachers can access metadata reports that indicate the standards that each assessment item addresses. These reports are found by accessing the Assessments menu, selecting the desired module Test Bank, and right clicking on the three dots to the right of the desired test and selecting Export Metadata. The metadata report will be located under My Downloads.The online materials do not have the standards linked to the questions.  However, the Teacher Edition does have a list of standards associated with the tests provided.

##### Indicator {{'3p.ii' | indicatorName}}
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials reviewed for Reveal Math Integrated meet 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.
• Each module contains a Performance Task, which includes a scoring rubric. The rubric provides the expectations for student responses to the task and a suggested scoring guide based on student responses. The Performance Task and Rubric are located on each module’s landing page under Review and Assess.
• The online Printable Module Tests contain answer keys and are located on each module’s landing page under Review and Assess: On-Level Assessments (Form A) and Differentiated Assessments (Forms B and C).
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials reviewed for Reveal Math Integrated provide opportunities for students to monitor their progress.

• At the beginning of each Module, students are provided with a “What Will You Learn?” document that includes 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.

#### 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 Integrated 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, strategies for meeting the needs of a range of learners, tasks with multiple entry points that can be solved using a variety of solution strategies or representations, support, accommodations, and modifications for English Language Learners and other special populations, and opportunities for advanced students to investigate mathematics at a deeper level.

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

The instructional materials reviewed for Reveal Math Integrated meet 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 include 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 reviewed for Reveal Math Integrated meet 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, and Remediation and Extension Tasks.
• 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 reviewed for Reveal Math Integrated meet 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 provide 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 reviewed for Reveal Math Integrated meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations.

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

The instructional materials reviewed for Reveal Math Integrated meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. There are multiple opportunities to address the needs of advanced learners. Extensions are included that present students with opportunities for problem solving, and examples include:

• In Integrated Math I, Module 2: Equations in One Variable, Lesson 5, Extension, students work with absolute value equations with variables on both sides of the equal sign, whereas during the preceding lesson, students worked with absolute value equations with variables on only one side of the equal side.
• In Integrated Math II, Module 1: Relationships in Triangles, Lesson 2, Extension, students extend their learning of angle bisectors from the lesson to create an inscribed circle within a triangle.
• In Integrated Math III, Module 1: Quadratic Functions, Lesson 7, Extension, students extend their learning of graphing a quadratic inequality from the lesson to graphing a set of quadratic inequalities.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials reviewed for Reveal Math Integrated provide 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 reviewed for Reveal Math Integrated provide opportunities for teachers to use a variety of grouping strategies. Throughout the lessons, the materials use an identifiable symbol for whole group, small group, and individual instruction. These icons are posted at the top of the teacher 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 reviewed for Reveal Math Integrated 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.
• There is a Spanish Interactive Student Edition eBook.
• The online multilingual eGlossary, located in the Program Resources: Glossaries after the last module in each course, includes terms and definitions from 14 different languages: English, Spanish, Arabic, Bengali, Brazilian Portuguese, Chinese, French, Haitian Creole, Hmong, Korean, Russian, Tagalog, Urdu, and Vietnamese.
• Each module includes a Cultural Connections resource, located on each module’s landing page under Additional Resources. Teachers may use these resources to point out the contributions people of various cultures have made in the history of mathematics.

#### Criterion 3.5: Technology Use

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 Integrated: 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; can be customized for individual learners and local use; and provide 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 Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed for Reveal Math Integrated 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 reviewed for Reveal Math Integrated 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.
##### Indicator {{'3ac.i' | indicatorName}}
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

The instructional materials reviewed for Reveal Math Integrated 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.
##### Indicator {{'3ac.ii' | indicatorName}}
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 reviewed for Reveal Math Integrated can be customized for local use.

• The materials provide differentiated intervention, and teachers can customize the lesson presentation by resequencing resources within a single lesson, adding their own resources, or removing resources from the presentation.
• There is 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 to 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 reviewed for Reveal Math Integrated provide an opportunity for teachers to collaborate with other teachers or students to collaborate with other students via technology. Teachers using Google Classroom can share assignments with other teachers by linking their Google account to their MHE account. Teachers using Google Docs can share assignments with students and assign linked Google docs through the MHE platform. In the Assignments menu, teachers can click on the three dots next to each assignment and share with Google Classroom.

##### 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 reviewed for Reveal Math Integrated 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 the real world.
• Personal Tutor videos are in Reflect and Practice 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, 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 Integrated | Math

#### Math High School

The instructional materials reviewed for Reveal Math Integrated meet the expectations for alignment to the CCSSM for high school, Gateways 1 and 2. In Gateway 1, the instructional materials meet the expectations for focus and coherence, and the instructional materials show strengths in attending to the full intent of the mathematical content contained in the high school standards, spending the majority of time on the CCSSM widely applicable as prerequisites, letting students fully learn each non-plus standard, engaging students in mathematics at a level of sophistication appropriate to high school, and explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. In Gateway 2, the instructional materials meet the expectation for reflecting the balances in the Standards and helping students meet the Standards' rigorous expectations by giving appropriate attention to procedural skills, conceptual understanding, and applications. Also in Gateway 2, the instructional materials meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

##### High School
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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###### Usability
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