## Alignment: Overall Summary

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Alignment to the CCSSM. The materials meet expectations for all of the indicators in Focus and Coherence (Gateway 1), and the materials meet expectations for all indicators in Rigor and Mathematical Practices (Gateway 2).

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## Gateway 1:

### Focus & Coherence

0
9
14
18
18
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
9
14
16
16
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
17
24
27
25
24-27
Meets Expectations
18-23
Partially Meets Expectations
0-17
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

+
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Gateway One Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; attending to the full intent of the modeling process; spending the majority of time on content widely applicable as prerequisites; allowing students to fully learn each standard; engaging students in mathematics at a level of sophistication appropriate to high school; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.

### Criterion 1a - 1f

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”.

18/18
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; attending to the full intent of the modeling process; spending the majority of time on content widely applicable as prerequisites; allowing students to fully learn each standard; engaging students in mathematics at a level of sophistication appropriate to high school; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.

### Indicator 1a

Materials focus on the high school standards.

### Indicator 1a.i

Materials attend to the full intent of the mathematical content in the high school standards for all students.

4/4
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Examples of standards that are attended to fully by the materials include:

• N-CN.1,2,7: The introduction of rational exponents is done in Math 1, Lesson 2.4 as students analyze conjectures about how rational numbers between whole number data points are approximated to develop a continuous exponential function from a discrete geometric sequence. In Math 2, Lesson 3.5, students are formally introduced to complex numbers and operations with complex numbers as they relate to solutions to quadratic equations.

• A-SSE.3: In Math 2, Lesson 3.7, students verify different forms of a quadratic expression to solve a given equation. Students explain how the factored form helps to reveal the zeros and what that means in the context of the question. In Math 1, Lesson 2.6, students are guided through an exploration of how expressions with different rational exponents are equivalent yet highlight different mathematical properties.

• A-APR.1-3: These standards are addressed in Math 3, Lessons 3.3-3.8 and Lesson 3.10. In Lesson 3.3, students add and subtract polynomials algebraically and graphically while also making and testing conjectures about the sum and difference of polynomials. In Lesson 3.4, students multiply polynomials using area models and traditional algebraic methods. Students divide polynomials using long division in Lesson 3.5 and use the Remainder Theorem to determine if a divisor is a factor of a polynomial. In Lesson 3.7, students investigate the relationship between roots, zeros, and x-intercepts using cubic functions. Students write cubic functions in factored form in order to identify the roots. In Lesson 3.8, students find real and complex imaginary roots of polynomials and write the polynomials in factored form.

• F-IF.3: In Math 1, Lesson 2.1, students work with arithmetic and geometric sequences including discrete and continuous linear and exponential situations. In Math 1, Lesson 2.2 students connect context with domain and use the domain to distinguish between discrete and continuous functions. In Math 1, Lesson 2.3, students name functions based on identifying the change over equal intervals to prove that the function is either linear or exponential.

• F-IF.7: In Math 1, Lesson 2.5, students apply their understanding of negative exponents to identify key features of the graphs of exponential functions. In Math 2, Lessons 4.1-4.4 students interpret and create graphs of piecewise functions then connect their understanding of piecewise functions to linear absolute value functions. In Math 3, Lesson 6.4, students make connections between an equation that models the height of a rider on a Ferris wheel to the amplitude, period, and midline of the graph of the function.

• G-MG.1: In Math 3, Lesson 5.3, Retrieval Ready, Set, Go, Problems 10-11, students use a model to find the total surface area and volume of the Washington Monument.

• S-CP.A: In Math 2, Lessons 10.1 and 10.2 students use samples to estimate probabilities. In Math 2, Lesson 10.5, students examine independence of events using two-way tables, and in Math 2, Lesson 10.6 students use data in various representations to determine independence.

### Indicator 1a.ii

Materials attend to the full intent of the modeling process when applied to the modeling standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The materials provide opportunities for students to engage in the modeling process. Additionally, all the modeling standards are addressed in 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:

• Math 1, Lesson 1.2, “Growing Dots,” addresses standards F-BF.1 and F-LE.1, 2, and 5. The students describe a given pattern and predict how the pattern would change after 3 minutes, 100 minutes, and “t” minutes. The teacher notes prompt the teacher to ask students to share out specific strategies and solution paths. While the teacher notes are scripted and prompt the teacher to seek out specific strategies, the problem leaves students open to any approach they find logical. The teacher notes place equal value in any of the possible student strategies and encourage students to analyze and discuss the varying strategies.

• Math 1 Lesson 4.2 “Elvira’s Equation,” addresses standards A-SSE.1, A-CED.4, and A-REI.3. Students use notes from the manager of the cafeteria to fill out a chart related to a large number of aspects of the daily lunch process. Students must give each item measured a variable notation, describe the quantity being measured (pizza) and the unit to be used (a slice). When the table is complete students write equations that model questions that the manager needs answered.

• Math 2, Lesson 1.3, “Scott’s Macho March,” addresses standards F-BF.1, F-LE.A, A-CED.1 and 2, and F-IF.4 and 5. Details about the number of push-ups Scott completes a day are provided, and students interpret the information, formulate a strategy, and compute their answers. Students extrapolate how the pattern will continue into the future as they are looking at the sum of the number of pushups that Scott has completed on a particular day. The teacher notes provide instructions for teachers to have students share out their answers, interpret what their answers mean in context, and evaluate each other’s answers and strategies.

• Math 2, Lesson 4.1 “Going to Pieces,” addresses standards F-IF.2 and F-IF.5-8. Students are given a piecewise function graph that purports to show the route of a pizza delivery car labeled only with ordered pairs at the end of each piece. Students must interpret the function related to the various activities of the driver, (traveling, sitting still, etc), then write a piecewise description of what they observed and a function to define it, including domains. Students also make observations about fuel efficiency related to the “traveling” sections of the graph.

• Math 3, Lesson 5.4, “You Nailed It,” addresses standards G-MG.1, 2, and 3. In this task, the students find the volume of an individual nail in order to estimate buying nails by the pound. Students use that information to calculate how many nails would be necessary for a particular building project and the cost of the nails. Students design a deck that will minimize the cost of materials, write an argument for the cost of materials, and defend their decisions to the whole class.

• Math 3, Lesson 7.3, “Getting on the Right Wavelength” addresses standards F-TF.5 and F-BF.3. Based on a given picture of a ferris wheel along with a few details, students write equations to model the height of the rider at any given time and make predictions about how the wheel will behave in the future.

### Indicator 1b

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

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers. Examples of how the materials allow students to spend a majority of their time on the WAPs include:

• A-SSE: Throughout the series, students engage with content related to the widely applicable prerequisites in A-SSE. Work related to the content standards found in this domain can be found in each course as both focus standards and supporting standards. For example, in Math 1, Lesson 2.10, students interpret the expression 2(n-1)as it relates to a given pattern. In Math 2, Lessons 2.3-2.6, students factor and rewrite expressions as directed in A-SSE.2. In Math 2, Lesson 9.2, students complete the square to reveal its center and radius (A-SSE.3b). In Math 3, Lesson 2.6, students interpret complicated expressions by viewing one or more of their parts as a single entity (A-SSE.1b). Students routinely factor polynomials of different powers in order to highlight different aspects of the function both algebraically and graphically.

• F-IF: Across the series, students engage with content related to the widely applicable prerequisites from this domain. For example, in Math 1, Lesson 1.7, students develop recursive and explicit functions and use them to find values of different terms in the sequence. In Math 1, Lesson 3.5, students match functions represented graphically, verbally, numerically, and analytically using cards containing important information about the functions. The information includes domain, range, values of functions at certain input values, comparisons of two functions, rate of change analysis, intercepts, and information about increasing, decreasing, and maximums. In Math 2, Lesson 2.9, students graph functions showing or describing key features such as the vertex, line of symmetry, intercepts, and transformations. In Math 3, Lesson 8.2, students reason and predict what graphs of functions have been built by combining functions of different types through addition and multiplication. Students graph the functions and identify key features of the graph.

• G-CO.9: In Math 2, students work with content related to standard G-CO.9. In Math 2 Lesson 5.5, students develop proofs that show that points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment. In Math 2, Lesson 5.7, students prove that vertical angles are equal.

• G-SRT: In Math 2, Lesson 6.2 students build upon their understanding of dilations developed in 7th and 8th grade to solidify their understanding of dilations and how triangles are similar. In Math 2, Lesson 6.3 students use the AA, SSS, and SAS Similarity Theorems to prove that triangles are similar. In Math 2, Lesson 6.5 students practice applying theorems about lines, angles and proportional relationships. In Math 2, Lesson 6.7 students apply prior understandings about similar triangles to develop the definitions of the trigonometric ratios. In Math 2, Lessons 6.8 to 6.10 students continue to work with right triangles, trigonometric relationships and methods for finding missing angles and sides in right triangles and applied problems.

• S-IC.1: In Math 3, Lessons 9.6 and 9.8-9.12, students compare different sampling methods and types of studies and address what kinds of conclusions can be reached when using the different types of studies. Students form conclusions given specific sets of data. This standard serves as a supporting standard for Lessons 9.8-9.12 as students work with confidence intervals and determine whether their results are statistically significant.

### Indicator 1b.ii

Materials when used as designed allow students to fully learn each standard.

4/4
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for, when used as designed, letting students fully learn each non-plus standard. In general, 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-APR.4: In Math 2, Lesson 6.6, Retrieval Ready, Set, Go Problems 1-5, students apply the Pythagorean Theorem to find the unknown lengths in figures. In Math 2, Lesson 7.7, Problems 9-11, students engage with the difference of squares. In Math 3, Lesson 3.9, Retrieval Ready, Set, Go, Problems 9-12, students engage with the sums and differences of cubes. Students do not use proven polynomial identities to describe numerical relationships.

• F-IF.6: In Math 1, Lesson 2.9, Retrieval, Ready, Set, Go, Problems 3-7, students use both linear and exponential functions to calculate the average rate of change and, in Problems 10-17, students use a given exponential graph and student-generated equations to calculate the average rate of change. The materials have limited opportunities for students to estimate the average rate of change from a graph.

• F-IF.7b: Students are given limited opportunities to graph square root, cube root, and cubic functions by hand or using technology throughout the series. Work with cubic equations is limited to Math 3, Lesson 3.2 in which students graph cubics, check their graphs with technology, and compare cubic graphs to quadratic graphs.

• F-TF.8: In Math 2, Lesson 6.8, Problem 14, students reason about the Pythagorean identity. In Math 3, Lesson 7.5, Problem 3, students use a right triangle to show that the same Pythagorean identity is true for all acute angles. Students have a limited number of opportunities to learn how to find the trigonometric value of angles in all of the four quadrants using the Pythagorean identity.

### Indicator 1c

Materials require students to engage in mathematics at a level of sophistication appropriate to high school.

2/2
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-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. Students engage in investigations throughout each task that utilize real-world contexts appropriate for high school use.

Examples of the materials using age-appropriate contexts include:

• In Math 1, Lesson 9.3, students analyze the Census Bureau’s income data to understand more about the differences between women’s and men’s salaries. Based on the data in this task and Lesson 9.2, “Making More \$”, students make a case to support whether the difference in income may be explained by differences in education or discrimination and consider what other data would be useful. (S-ID.6-8)

• In Math 2, Lesson 10.3, students use data from a restaurant to predict how much food to prepare in order to avoid too much waste by computing conditional probabilities and applying the addition rule. (S-CP.1,7)

• In Math 3, Lesson 6.5, students continue to use the ideas, strategies, and representations discovered when completing the Ferris wheel tasks from the previous lessons. Students describe the periodic motion of the rider’s shadow on the Ferris wheel as the shadow moves back and forth across the ground when the sun is directly overhead. Students apply the cosine function to determine the distance horizontally from the center of the wheel and derive the function horizontal position of the shadow =25 cos (18x) . (F-IF.7e, F-TF.2,5)

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

• In Math 1, Lesson 3.4, students use a given graph of two functions to answer questions regarding key features of the graph, and students interpret some of the key features. This is an application of a key takeaway from Grades 6-8 in applying basic function concepts to develop/solidify new understanding in this unit (A-APR.1, A-CED.3, A-REI.11, F-IF.7).

• In Math 2, Lesson 6.1, students consider a scenario where an employee at a copy center is enlarging a photo for a customer and makes a mistake. Students answer questions to determine what the mistake was and how the employee should have enlarged the photo. Students apply a key takeaway from Grades 6-8 regarding similar figures (G-SRT.1).

Examples of the materials using various types of real numbers include:

• In Math 1, Lesson 2.6, students verify that the properties of integer exponents also apply to rational exponents. Students use exponent rules to write equivalent forms of expressions involving rational exponents and rational bases. Expressions include rational numbers in the base as well as in exponents (N-RN.1,2, A-SSE.3).

• In Math 2, Lesson 1.6, students distinguish between relationships that are quadratic, linear, exponential or neither. The materials include relationships presented with tables, graphs, equations, visuals, and story context. Students also create a second representation for the relationships given. Graphing technology is recommended for this task. The contexts provided and the numbers used in the equations and graphs are all appropriate for high school students. (F-IF.4,5,9, F-LE.A)

### Indicator 1d

Materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Overall, the materials include connections that are intentional and thoughtful as the tasks are reexamined so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the materials is designed to spiral concepts throughout the entire series.

Examples of the materials fostering coherence through meaningful mathematical connections in a single course include:

• In Math 1, Lessons 2.1-2.3, students analyze and build linear functions to model different scenarios. They represent the functions numerically, graphically, and analytically and focus on looking for the constant rate of change in linear functions. In Math 1 Lessons 9.1-9.5, students analyze bivariate data represented in tables and scatter plots. They apply what they learned about linear relationships earlier in Math 1 to identify which variables may have linear relationships and interpret the meaning of the slope and y-intercept of linear models. Students also change data to get the correlation coefficient to reach a given value by either making the data more or less linear. This allows them to use what they know about constant rates of change and linear functions. Additionally, students reference residual plots to see what characteristics may indicate linear or non-linear relationships. (F-BF.1, F-LE.1a-c,2, S-ID.6a-c,7,8)

• In Math 2, Lesson 3.1, Students solve quadratic equations by applying knowledge of quadratic function behavior developed in Math 2, Units 1 and 2. Students discover that factoring a quadratic expression and completing the square are ways to not only find zeros and the vertex of a function, but to find solutions to a quadratic equation as well. In Math 2, Lesson 3.2, students build on the knowledge from Lesson 3.1 to derive the quadratic formula. In Math 2, Lesson 3.3, students synthesize learning from the first two lessons to solve a system consisting of a quadratic and linear equation. Students apply algebraic methods to solve the system and then show the solution graphically. In the remaining lessons of Math 2, Unit 3, students solve quadratic equations that result in both irrational and complex solutions. (N-CN.7, A-SSE.3a,b, A-CED.1,4, A-REI.4,7,10)

Examples of the materials fostering coherence through meaningful mathematical connections between courses include:

• In Math 1, Lesson 1.4, “Scott’s Push-Ups'' students analyze the pattern of push-ups Scott will include in his workout. Students examine tables, graphs, and recursive and explicit formulas that focus on how the constant difference is represented in different ways and define the function as an arithmetic sequence. In Math 2, Lesson 1.3, “Scott’s Muscle March” students revisit Scott’s workout, but this time his push-up pattern creates a quadratic model. Again, students use algebraic, numeric, and graphical representation to represent a story with a visual model. In Math 3, Lesson 3.1, “Scott’s March Motivation” students develop an understanding of how the degree of a polynomial determines the overall rate of change. (A-CED.1,2, F-IF.4,5, F-BF.1, F-LE.1,2,3,5)

• In Math 3, Lesson 6.6, “Diggin’ It” students discover alternative ways of measuring a central angle of a circle: in degrees, as a fraction of a complete rotation, or in radians. Students use right triangle trigonometry to find the coordinates of points on a circle and use the relationship between arc length measurements and radian angle measurements all within the context of an archeological dig. This task builds upon what students learned in Math 2, Lesson 8.4 where students encountered the idea that the length of an arc intercepted by an angle is proportional to the radius and defined the radian measure of the angle as the constant of proportionality. In Math 3, Lesson 6.7, “Staking It,” students’ previous understanding of radians as the ratio of the length of an intercepted arc to the radius of the circle on which that arc lies and uses radian measurement as a proportionality constant in computations. (F-TF.1,2, G-C.5)

### Indicator 1e

Materials explicitly identify and build on knowledge from Grades 6-8 to the High School Standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The materials explicitly identify the standards from Grades 6-8 in the Progression of Learning section of the teacher materials. This information appears routinely in the design of the teacher materials but not in the student materials.

Examples where the teacher materials explicitly identify standards from Grades 6-8 and build on them include, but are not limited to:

• In Math 1, Lesson 1.1, the Progression of Learning states, “Beginning in grade 7 (7.EE.A.2), students have used variables to describe a changing quantity.” Students create algebraic expressions to model patterns and identify different parts of the expression in terms of what those parts represent in the problem (A-SSE.1) which builds on work students did in Grade 7 rewriting expressions to shed light on problems and how quantities are related (7.EE.2).

• In Math 1, Lesson 3.1, students make connections to the key features of graphs of functions listed in F-IF.4 by connecting the features to a situation using the water level of a pool over a period of time. The Progression of Learning references that this lesson builds on students’ experience with functions in Grade 8 (8.F.1-5) by expanding the concepts to different functions and developing the key features to use as tools for analysis in future lessons.

• In Math 1, Lesson 4.1, the Progression of Learning states, “Students were introduced to solving one- or two-step equations related to the context of a word problem in grade 7 mathematics (7.EE.B.4). Students have also learned how to interpret the order of operations when evaluating an expression in grade 6 (6.EE.A.2), and will need to draw upon that understanding in today’s lesson." Students build on that knowledge by developing strategies to solve multi-step equations.

• In Math 2, Lesson 6.6, the Progression of Learning identifies 8.G.6 and 8.G.7 as students’ first encounter the Pythagorean theorem. It also mentions students’ prior work with solving proportional statements in Grade 7 (7.RP.2c, 7.RP.3). Students build on this prior knowledge in this lesson as they develop right triangle trigonometric ratios. The application of the previous understandings of the Pythagorean theorem continues into Math 3, Lesson 7.5 as students derive and justify the Pythagorean identity.

• In Math 2, Lesson 10.1, the Progression of Learning states, “In grade 7, students learned to develop probability models based on data and to find the probability of compound events with tables, tree diagrams and simulations (7.SP.6, 7.SP.7a,b, 7.SP.8a, b, c). This lesson builds on students’ experience with using tree diagrams to find probabilities to introduce conditional probability.” Students write and interpret conditional probability statements in the context of medical testing.

### Indicator 1f

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.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do explicitly identify the plus standards and do use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready.

Throughout the series the plus standards are included in such a manner that they can be studied simultaneously with the non-plus standards. In the Course Materials Guidance document, the following statement addresses the inclusion of plus standards in lessons primarily aligned to non-plus standards: “Some non-enrichment lessons may include (+) standards and /or (^) [mathematics that goes beyond the expectations of the standards] if the content is related to the mathematics of the lesson and can be explored simultaneously with the non-plus standards of the lesson. Enrichment lessons are distributed throughout the curriculum as natural extensions of the mathematics of the units. Consequently, the mathematical ideas of the Enrichment lessons are accessible to all students.” Lessons which are identified as enrichment (E) which are primarily aligned to plus standards can be easily omitted if necessary. Plus standard activities included in non-enrichment lessons, however, may not be as easily omitted.

Examples of components of the materials that address the plus standards include:

• N-CN.8: In Math 2, Lesson 3.4, students use the quadratic formula to find non-real roots and write the equation of the parabola in factored form. In Math 3 Lesson 3.10, students find suitable factorizations of quadratic, cubic, and quartic polynomials; some of these have imaginary roots and develop understanding that imaginary roots occur in conjugate pairs.

• N-CN.9: In Math 2, Lesson 3.4, students engage with the complex solutions, the Fundamental Theorem of Algebra, and the relationship between roots and factors. These themes are extended throughout Math 3, Unit 3. The materials include problems that are tagged with “(+)” to indicate alignment to the plus standard.

• A-APR.5: In Math 3, Lesson 3.4, students begin by reviewing how to multiply polynomials and end with by applying Pascal’s Triangle to expand binomials.

• A-APR.7: In Math 3, Lessons 4.4 and 4.5, students perform operations with rational expressions.

• A-REI.9: In Math 1, Lessons 8.9 and 8.10, students use the inverse of the coefficient matrix to solve systems of linear equations.

• F-IF.7d: In Math 3, Unit 4, students graph rational functions, identify zeros and asymptotes, and show end behavior.

• F-BF.1c: In Math 3, Lessons 8.4, 8.5, and 8.6, Retrieval Ready, Set, Go, students compose functions.

• F-BF.4b: In Math 3, Lesson 1.4, students find the inverse of linear, quadratic, and exponential functions, apply verbal descriptions to the inverse operations, and generalize an algebraic process for finding inverses. In Lesson 1.5, students continue to find inverse functions and verify the inverse functions with an alternate use of composition (“The function g is the inverse of function f if and only if f(a)=b and g(b)=a”). In Math 3, Lesson 1.5, Retrieval Ready, Set, Go, students use composition to verify that functions are inverses of each other.

• F-BF.4c: In Math 2, Lessons 4.5 and 4.6, students create multiple representations, including graphs and tables, of given functions and determine if there is a relationship between the functions, which develops into recognizing inverse functions. In Math 3, Lesson 1.2, students find inverse functions to quadratic and square root functions, and, in Lesson 1.3 find inverse functions for exponential functions. Lesson 1.5 provides students additional practice with finding inverses.

• F-BF.4d: In Math 3, Lesson 1.2, students produce an invertible function from a non-invertible function by restricting the domain.

• F-BF.5: In Math 3, Lesson 1.3, students learn that the inverse of an exponential function is a logarithmic function. In Math 3, Lesson 2.5, students solve base 10 exponential equations using logarithms graphically and algebraically.

• F-TF.3,4: In Math 3, Lesson 7.4, students use the unit circle diagram to find tangent values for angles that are multiples of the angles found in the special right triangles. Later in Unit 7, students explain why the sine, cosine, and tangent functions are even or odd using reasoning based on the unit circle, graphs of the functions, and prior knowledge of the trigonometric even and odd identities.

• F-TF.7: In Math 3, Lesson 7.6, students use trigonometric identities and inverse functions to solve trigonometric equations.

• G-SRT.9-11: In Math 3, Lessons 5.6-5.7, students find missing sides and angles of non-right triangles using a variety of strategies leading to the development of the Law of Sines and the Law of Cosines. In Math 3, Lesson 5.8, students derive an alternate formula for the area of a triangle in terms of trigonometric functions.

• G-C.4: In Math 2, Lesson 7.4, students describe a procedure for constructing a tangent line through a point outside the circle and then prove the procedure works.

• G-GMD.2: In Math 2, Lesson 8.8, students make an informal argument using Cavalieri’s principle for the formulas for the volumes of solid figures.

• S-MD.7: In Math 2, Lesson 10.1, students analyze and make sense of tuberculosis skin test data using conditional probability.

The following plus standards are not addressed in the series:

• N-VM.4b,4c,5a,5b

• S-CP.8,9

• S-MD.1-6

## Rigor & Mathematical Practices

### Criterion 2a - 2d

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.

8/8
+
-
Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Rigor and Balance. The materials meet expectations for providing students opportunities in developing conceptual understanding, procedural skills, and application, and the materials also meet expectations for balancing the three aspects of Rigor.

### Indicator 2a

Materials support the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Every unit attends to the learning cycle, interweaving aspects of mathematical proficiency. Most of the lessons across the series are exploratory in nature and encourage students to develop understanding through questioning and various activities. Concepts build over many lessons within and between courses in the series. Examples include:

• N-RN.A: In Math 1, Unit 2, a contextual situation offers students the opportunity to understand how values of a dependent variable can exist on the intervals between the whole number values of the independent variable for a continuously increasing exponential function. Next, students examine the role of positive and negative integer exponents and begin to understand the need for rational exponents. Students further develop their conceptual understanding by verifying that the properties of integer exponents remain true for rational exponents.

• A-APR.B: In Math 3, Unit 3, students develop an understanding of multiplicity and a deeper understanding of the relationship between the degree and the number of roots of a polynomial. Then, students use their background knowledge of quadratic functions and end behavior to extend their understanding to higher-order polynomials. The polynomials in this unit are factorable and allow students opportunities to solidify their understanding of end behavior, the Fundamental Theorem of Algebra, the multiplicity of a given root, and what the multiplicity would look like graphically. Finally, students extend their understanding of the Fundamental Theorem of Algebra and the nature of roots by applying the Remainder Theorem.

• A-REI.A,B: Math 1, Unit 4 builds students’ conceptual knowledge by first introducing multivariable linear equations and then having students express given relationships in equivalent forms. Students engage with inequalities as they encounter the contextual need for inequalities. Students consider the differences and similarities between solving inequalities and solving equations, including that inequalities produce a range of solutions, the inequality symbol must be changed when multiplying or dividing by a negative number, and the reflexive property is true only for equations.

• G-GPE.1: Math 2, Lesson 9.1, students cut out triangles and pin them to a coordinate plane to build a unit circle effectively developing their understanding of the relationship between the Pythagorean Theorem and the equation of a circle at the origin. Students connect their geometric understanding of circles as the set of all points equidistant from a center to the equation of a circle. This task focuses on a circle (constructed of right triangles) with a radius of 6 inches in order to focus on the Pythagorean theorem and use it to generate the equation of a circle centered at the origin. After constructing a circle at the origin, students consider how the equation would change if the center of the circle is translated.

• G-GPE.5: In Math 1, Lesson 8.3, students prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. The proofs use the ideas of slope triangles, rotations, and translations and are preceded by a specific case that demonstrates the idea before students are asked to follow the logic using variables and thinking more generally.

• G-GPE.6: In Math 1, Lesson 8.2, students use similar triangles and proportionality to find the point on a line segment that partitions the segment in a given ratio. Students first find the midpoint of a segment using two possible strategies and use similar triangles to find segments in ratios other than 1:1. The formula for finding the midpoint of a segment is formalized during the discussion. The discussion can also be extended to derive a formula for finding the point that partitions a segment in any given ratio.

### Indicator 2b

Materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. The instructional materials develop procedural skills and students independently demonstrate procedural skills throughout the series. Examples include:

• N-CN.7: In Math 2, Lesson 3.4, students write 10 equations in vertex form, standard form and factored form. Five of these equations have complex roots. In Math 2, Lesson 3.5, students find complex roots of quadratic equations in problems 11, 13, and 14. In Math 2, Lesson 3.5 Retrieval Problem 2 has a complex solution and Go Problems 28, 31, and 32 have complex solutions. Additional practice is provided in the RRSG problem sets for Lessons 3.6-3.8.

• A.APR.2: In Math 3, Lesson 3.5 students explore the relationship between the remainder and factor in problems 3-8 and make conjectures based on their work. In Math 3, Lesson 3.5 RRSG, students practice this concept in the Set Problems 10-20.

• A-CED.4: In Math 1, Lesson 4.2 students apply the equation solving process to solve literal equations and formulas. There are multiple opportunities to solve a formula for a given variable throughout the lesson and several practice examples in the RRSG exercises. Students are presented with multiple opportunities to practice this standard in the RRSG throughout the remainder of Math 1, Unit 4. Additionally, practice for this standard is also found in the RRSG exercises of Math 1, Lessons 5.5, 8.3, and 9.5. The standard is revisited in Math 2, Lessons 4.4 and 4.6.

• G-GPE.7: In Math 1, Lesson 8.1, students calculate the length of ribbon needed to create a specific pattern. Students then find the perimeter of a hexagon in a different pattern. In RRSG Set Problems 9-12 students find the perimeter of two triangles and two quadrilaterals. In Math 2, Lesson 9.3 RRSG Retrieval Problem 1 and Ready Problems 1-4 students also find the perimeter of polygons using ordered pairs in the coordinate plane.

• S-CP.3: In Math 2, Unit 10, students investigate conditional probabilities in a wide variety of different contexts and using different models such as tree diagrams, Venn diagrams, two-way tables, and formulas. Students then use what they know about conditional probabilities to determine whether events are independent. There are many opportunities for students to practice in the student tasks and Retrieval Ready, Set, Go (RRSG) problem sets.

### Indicator 2c

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series 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 use real-world situations in which students can apply mathematical concepts. In situations where a real-world context is not immediately appropriate, the materials begin with abstract situations (graphs, dot models, etc.) and build to the application of the concept in a real-world situation in a later task. Every lesson involves a task, and every task is a real-world situation or a mathematical model that builds to a real-world situation.

The series includes numerous applications across the series, and examples of select standards that specifically relate to applications include, but are not limited to:

• A-CED.3: In Math 1, Lessons 5.1 and 5.2, the pet-sitting problem uses systems of equations and inequalities to build a business model, minimize costs, and maximize profit.

• F-IF.4,5: In Math 1, Lesson 3.2, students use tables and graphs to interpret key features of functions (domain and range, where function is increasing/decreasing, x and y intercepts, rates of change, discrete vs. continuous) while analyzing the characteristics of a float moving down a river. Students interpret water depth, river speed, and distance traveled using the function skills they are developing.

• F-BF.1: In Math 2, Lesson 1.2, students develop a mathematical model for the number of squares in the logo for size n. Students are encouraged to use as many representations as possible for their mathematical model.

• F-TF.5: In Math 3, Lesson 6.2, students use the Ferris wheel to determine how high someone will be after 2 seconds, after observing that the Ferris wheel makes one complete rotation counterclockwise every 20 seconds. Students are continuing the work from a previous task in Math 3, Lesson 6.1. Students then determine elapsed time since passing a specific position. Students generate a general formula for finding the height of a rider during a specific time interval and are then asked how they might find the height of the rider for other time intervals.

### Indicator 2d

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Overall, the three aspects are balanced with respect to the standards being addressed. 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, developing procedural skill and fluency, and providing engaging applications.

The materials engage students in each of the aspects of rigor in a pattern that repeats itself throughout the materials. Each unit contains Developing Understanding (conceptual understanding), Solidifying Understanding, Practicing Understanding tasks, in addition to the Retrieval Ready, Set, Go (procedural skill) problem sets.

For example, Math 1, Lesson 2.1, a Developing Understanding Task, focuses on conceptual understanding as students build upon their experiences with arithmetic and geometric sequences and extend to the broader class of linear and exponential functions with continuous domains. Students compare these types of functions using various representations (table, graph, and equation). In Math 2, Lesson 2.2, a Solidifying Understanding Task, students discern when it is appropriate to represent a situation with a discrete or continuous model, thus deepening conceptual understanding. This task also has students practice modeling with mathematics by connecting the type of change (linear or exponential) with the nature of that change (discrete or continuous) which develops students’ procedural skill and fluency. Throughout both tasks, problems are presented to students within real-world contexts (medicine metabolized within a dog’s bloodstream, library re-shelving efficiency, e-book download rate, savings accounts, pool filling, pool draining, etc), so students learn the mathematical concepts and procedures through the application of the mathematics.

### Criterion 2e - 2h

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

8/8
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Practice-Content Connections. The materials intentionally develop all of the mathematical practices to their full intent: make sense of problems and persevere in solving them (MP1), reason abstractly and quantitatively (MP2), construct viable arguments and critique the reasoning of others (MP3), model with mathematics (MP4), use appropriate tools strategically (MP5), attend to precision (MP6), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8).

### Indicator 2e

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for supporting the intentional development of overarching mathematical practices (MPs 1 and 6), in connection to the high school content standards. Overall, MP1 and MP6 are used to enrich the mathematical content and are not treated as individual mathematical practices. Throughout the materials, students are expected to make sense of problems and persevere in solving them while attending to precision. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Examples where students make sense of problems and persevere in solving them include:

• Math 1, Lesson 3.1: Students are able to make sense of creating graphs given a situation. Students are already familiar with graphing rate of change and continuous and non-continuous situations. This task addresses domain and step functions. Students persevere in creating graphs by analyzing what is happening during each interval of time on their graph.

• Math 2, Lesson 4.1: Students write piecewise linear functions and interpret piecewise functions presented in algebraic form. Throughout the task, students use the piecewise-defined function to make sense of the problem to identify key features of the function including average rates of change, domain, and other relative information connecting the context to the function.

• Math 3, Lesson 7.2: Students interpret a given function to answer questions about high tide, low tide, and the time between tide events. Students make sense of the problem by using multiple representations such as graphs, tables, the unit circle, and the meaning of the parameters of a periodic equation to answer these questions.

Examples where students attend to precision include:

• Math 1, Lesson 5.5: Students represent constraints in the context of a pet sitting business with inequalities and with systems of inequalities. Students find the point of intersection and must interpret its meaning in the context of cats and dogs. Students must attend to the language in the constraints. Students must recognize that time is measured in both minutes and hours in the constraints which require them to attend to the units they choose to use.

• Math 2, Lesson 7.1: Students attend to the precision of language by using correct mathematical vocabulary when describing and illustrating their process for finding the center of rotation of a figure consisting of several image/pre-image pairs of points.

• Math 3, Lesson 5.1: Students visualize two-dimensional cross sections of three-dimensional objects and draw the cross sections of those objects. Students are encouraged to use precise language as they work through the task in order to precisely identify components of the three-dimensional objects used.

### Indicator 2f

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. Overall, MP2 and MP3 are used to enrich the mathematical content found in the materials, and these practices are not treated as isolated experiences for the students. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Examples where students reason abstractly and quantitatively include:

• In Math 1, Lesson 5.1, students solve systems of linear equations using a variety of strategies. Then students use the solution to make decisions based on a context. Students decontextualize the contexts when working with a system of equations to represent pricing plans for each company. Students must attend to units and the meaning of operations used in the equations. Students then contextualize the solution to verify it makes sense in the context. Students reason abstractly and quantitatively which company to hire by using a table, a graph, and/or Algebra.

• In Math 2, Lesson 1.4, students write a function for a given context. Students must reason quantitatively to generate the function based on a numeric pattern. Students are required to consider two parameters, perimeter and area, and they must write the function for the area using one variable. Students will decontextualize the model in order to identify the key features and then relate the key features to the story context.

• In Math 3, Lesson 3.2, students identify the characteristics and graph the basic cubic function. Students will understand that the same transformations they used to graph quadratic functions can be applied to cubic functions. Students reason abstractly and quantitatively as they compare the rates of change and end behavior of quadratic and cubic functions. In the Retrieval, Ready, Set, Go practice set, students reason quantitatively by substituting in values to compare different power functions. They reason abstractly by making generalizations based on their knowledge of exponents.

Examples where students construct viable arguments and critique the reasoning of others:

• In Math 1, Lesson 3.2, students explain why they either agree or disagree with each observation Sierra made. Students listen to the reasoning of others and decide whether the reasoning makes sense. Students also justify or explain flaws in Sierra’s observations.

• In Math 2, Lesson 6.3, students read through Mia and Mason’s conjectures about similar polygons and decide which they believe are true. Students are also presented “explanations” from either Mia or Mason and must write an argument deciding whether they agree.

• In Math 3, Lesson 3.9, students find patterns in the end behavior of functions and describe the end behavior of functions using the appropriate notation. Throughout the task students will use prior knowledge, make conjectures, and develop a series of statements to describe the relationship between expressions as the input values approach various quantities. Students justify conclusions and respond to others by listening, asking clarifying questions, and commenting on the reasoning of others.

### Indicator 2g

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. Overall, MP4 and MP5 are used to enrich the mathematical content and are not treated as individual practices. Throughout the materials, students model with mathematics and use tools strategically. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Examples where students engage in modeling with mathematics include:

• In Math 1, Lesson 5.4, students use systems of equations, tables and graphs to model the start-up costs of a new business and the space available to board cats and dogs. Students write equations for the constraints in different forms and then identify what information each form reveals in the context of the situation.

• In Math 2, Lesson 10.3, students use Venn diagrams to model the situation, analyze the data, and write various probability statements (unions, intersections, and complements) and then apply the Addition Rule and interpret the answer in terms of the model.

• In Math 3, Lesson 6.1 students develop ways of thinking about the location of points around a circle, which become fundamental in their understanding of trigonometric functions, radian measure, and the unit circle. Students develop expressions to model the height of a rider at a particular angle. Students apply mathematics they know (right triangle trigonometry) to model motion around a Ferris wheel based on angles of rotation. Students use points to model the location of the rider.

Examples where students choose appropriate tools strategically include:

• In Math 1, Lesson 9.1 students strategically use graphing technology to interpret the correlation coefficient of a linear fit. Using technology, students also alter the data to see the effect on the scatter plot and correlation coefficient.

• In Math 2, Lesson 3.1, students solve quadratic equations graphically and using different algebraic techniques and make connections between solving quadratic equations and graphing quadratic functions. Throughout the student tasks, students have options for which method they would like to use. Sometimes the problems leave it up to the student to choose which method they would like to use, and specific methods are called out to be used in other problems. Students solve quadratic equations by factoring, completing the square, using inspection, graphing, and using symmetry. Students will have opportunities to select appropriate tools to use while solving and graphing. They can hand sketch graphs or construct graphs using graphing calculators or other digital platforms.

• In Math 3, Lesson 2.5, students solve exponential equations which would require the use of logarithms using tables and graphs. In the last part of the task, students solve systems of linear and exponential equations using a method of their choice. Students may choose to use calculators or other technology with base 10 logarithmic and exponential functions to complete the problems. Students are encouraged to make appropriate decisions about using technology, like finding exact values for log expressions without relying on a calculator when they can.

### Indicator 2h

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.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. Overall, MP7 and MP8 are used to enrich the mathematical content, and these practices are not treated as isolated experiences for the students. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

The materials frequently take a task from a previous course and add a new contextual layer to the mathematics, such as Math 1, Lesson 5.2, “Pet Sitters” and Math 3, Lesson 1.1, “Brutus Bites Back.” Students are constantly extending the structures used when solving problems that build on one another and, as a result, are able to solve increasingly complex problems. In the instructional materials repeated reasoning based on similar structures allows for increasingly complex mathematical concepts to be developed from simpler ones.

Examples where students look for and make use of structure include:

• In Math 1, Lesson 2.1, builds upon students’ previous experiences with arithmetic and geometric sequences to extend to the broader class of linear and exponential functions with continuous domains. Students use tables, graphs, and equations to create mathematical models for contextual situations. Students continue to define linear and exponential functions by their patterns of growth. Students repeatedly use similarities and differences between situations to define the appropriate expression structure.

• In Math 2, Lesson 4.3, students learn how to graph, write, and create linear absolute value functions by looking at structure and making sense of piecewise defined functions. They connect prior understandings of transformations, domain, linear functions, and piecewise functions and share strategies for how to go from one representation to another in order to graph and write equations for absolute value piecewise functions.

• In Math 3, Lesson 3.7, students use their background knowledge of quadratic functions and end behavior to extend their understanding of polynomials in general. The polynomials in this task are easily factorable and allow students opportunities to solidify their understanding of end behavior, the Fundamental Theorem of Algebra, and the multiplicity of a given root, and what that would look like graphically.

Examples where students look for and express regularity in repeated reasoning:

• In Math 1, Lesson 5.9, students practice solving systems of linear equations by obtaining systems of equivalent equations. By the end of the task, through repeated practice, students develop a procedure for solving a system of equations by elimination.

• In Math 2, Lesson 3.2, students work with specific examples of quadratic functions in order to identify a process for locating the x-intercepts relative to the axis of symmetry. Students use the repeated reasoning after working the specific examples to develop the quadratic formula.

• In Math 3, Lesson 6.6, students calculate the x and y coordinates for stakes placed on concentric circles as well as the arc length on each circle placed around an archeological site. In problems 3 and 4 students look for patterns in the tables created and the processes used to calculate points and identify what the repeated patterns imply.

## Usability

#### Meets Expectations

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Gateway Three Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Usability. The materials meet expectations for Criterion 1 (Teacher Supports), partially meet expectations for Criterion 2 (Assessment), and meet expectations for Criterion 3 (Student Supports).

### Criterion 3a - 3h

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

9/9
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials; contain adult-level explanations and examples of the more complex course-level concepts and concepts beyond the current courses so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

### Indicator 3a

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Each unit contains an Overview that provides teachers with information about what is taught and how it will be presented.  Each Overview begins with a discussion of where the students may have touched on the concepts in previous years, or in previous units of the course, and how the unit will build on that knowledge. It also provides a table that provides a summary of the mathematics in each lesson.

Each lesson is presented in a consistent format in order to provide teacher guidance on how to present the student materials in a way that engages students and guides their mathematical development. Examples of how the instructional materials provide guidance on how to present the materials include:

• In Math 1, Lesson 9.6, students review standard representations for single variable numerical data, compare how representations represent the data in different ways, and create their own representations of data given specific characteristics of center, shape, and spread. The Launch portion of the lesson includes a Notice and Wonder activity which provides detailed narratives and prompts for teachers to facilitate students’ work. In the Explore portion of the lesson, teachers are encouraged to pair students up or place them in small groups to discuss the sketches they have created. Also in the Explore portion, under the heading Selecting and Sequencing Student Thinking, teachers are guided to select two students who have sketches that meet the given criteria but are very different. The Teacher Notes state “For instance, select a student for 4b who has a distribution with median of 5 with two equal quartiles on either side and another student whose distribution has a median of 5 that has two different sized quartiles.”  The Discuss portion of the lesson allows students to present their graphs. The directions for the teacher guide them through possible student examples and how to use those examples as a part of a full class discussion that will enable students to address key takeaways of the lesson.

• In Math 2, Lesson 5.7, students practice writing proofs to show that conjectures are true. The Explore Narrative in the Teacher Lesson recommends that students work with a partner or in small groups. Teachers are reminded that “a variety of ways may be used to present the proof both in terms of the conceptual approaches they use (transformations, linear pairs, congruent triangle criteria) and in terms of the format they use to write their proofs (two-column, flow diagrams, narrative paragraphs, algebraic proof).” Additionally, teachers are reminded that they should select a variety of approaches when presenting work during the whole class discussion. The Monitor Student Thinking section in the Explore Narrative presents questions teachers can ask students if they notice that students are struggling with proof-writing.

• In Math 3, Lesson 3.3, students compare operations with polynomials to operations with integers and use those comparisons to add and subtract polynomials algebraically. The Launch Narrative in the Teacher Lesson guides the teacher to help students see how numbers are structured as the sum of powers of 10 while polynomials are structured as sums of powers of x. The Connect Student Thinking portion of the Launch Narrative describes the types of examples the teacher should select from student work to share with the class in order to highlight different approaches to answering the problems. In the Discuss Narrative, the Pause and Record routine included in the Selecting, Sequencing, & Connecting Chart guides the teacher through the Think-Pair-Share routine to have students identify the three most important things to remember about subtracting polynomials. The three important takeaways are also provided for the teacher.

Each Teacher Lesson includes Learning Goals (for the teacher), the Learning Focus (for the student), Standards for the Lesson, Materials (when necessary), Required Preparation, BLMs, Progression of Learning, and Purpose. Notes are provided for the teacher to anticipate, monitor, and connect student thinking. These notes also provide detailed information about how to be prepared for common student questions and to guide student work to ensure that key takeaways are reached and understood. There are narratives that break down the specific instructional strategies and what the students should be doing to get the most out of each task.

The Anticipate & Monitor Charts list solutions, misconceptions, and other possible ideas that students may have when completing the tasks. These charts also include follow up questions and suggestions of how to address misconceptions and to expand upon the solutions and other ideas offered by students.

The Selecting, Sequencing, & Connecting Charts provide some examples of how individual, small group, and full class discussions can be facilitated to use students’ answers and ideas to guide them toward reaching the goals of the lesson.

Examples of how the instructional materials provide teacher guidance on how to plan for instruction include:

• In Math 1, Lesson 5.3, in which students graph the solution set for linear inequalities in two variables, teachers are provided with a detailed Materials list including graph paper, colored pencils, graphing calculators, and a link to a GeoGebra app. The Launch Narrative discusses the possibility that “[s]tudents may need direct instruction in how to access these tech tools and may benefit from a list of steps to be able to use the applet or software.”

• In Math 2, Lesson 3.3, students develop fluency and flexibility in solving quadratic equations and determine the most efficient method for solving any quadratic equation. In the Required Preparation portion of the lesson, teachers are directed to work the task and consider given questions in order to Anticipate Student Thinking. In the Explore portion of the lesson, teachers are guided to provide sentence frames to support discussions (Math Language Routine 8: Discussion Supports).

### Indicator 3b

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for containing adult-level explanations and examples of the more complex course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The teacher edition contains thorough adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge. Each unit includes an overview of the content addressed in each lesson. The narrative is presented in adult language with a quick table reference of math concepts presented per lesson. In addition, each lesson’s Progression of Learning and Purpose sections describe specifically how lessons connect content throughout the learning cycles of multiple lessons. As a quick reference point, Open Up High School Math Dependency, a chart provided with the series, gives teachers the opportunity to see where a given lesson connects to another course in the series but not outside the scope of the current materials. Examples of course-level explanations include:

• In Teacher Notes, Purpose, there is information about a topic to be introduced. For example, in Math 2, Lesson 3.4, students are introduced to non-real solutions of a quadratic function. The Note in this lesson discusses a brief history of complex numbers including dates and names of mathematicians responsible for current notations.

• In Math 1, Unit 3, at the end of the Unit Overview, there is a paragraph on notation that explains the different ways to write interval notation and how interval notation connects to the set notation students have been using.

• In Math 2, Lesson 5.10, detailed information is provided in Teacher Notes regarding the medians, angle bisectors, and the perpendicular bisectors of triangles and how these points of concurrency relate to balance, inscribing a circle, and circumscribing a circle.

For each course, the materials also provide adult-level explanations and examples for teachers to improve their own knowledge of concepts beyond the current course through a collection of essays titled Connections to Mathematics Beyond the Course. These essays are also directly connected to the lessons with which they are relevant, and examples include:

• In Math 1, Lesson 2.9 is connected to Rate of Change.

• In Math 2, Unit 1 is connected to First and Second Differences.

• In Math 3, Lessons 9.9 and 9.10 are connected to Confidence Intervals.

### Indicator 3c

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

The teacher materials provide information to explain coherence across multiple courses and to enable teachers to make connections to prior and future content. Examples include but are not limited to:

• The Open Up High School Math Dependency Chart illustrates how units are connected in the series. For example, the chart shows that Math 3, Unit 6, Modeling Periodic Behavior depends on Math 3, Unit 1, Functions and their inverses. The document also includes Additional Dependencies. For example, Math 2, Unit 6 depends on Math 2, Unit 2 (algebra skills for working with quadratic expressions).

• In the Course Guide, the Standards Alignment for HS Integrated lists each lesson from the series that addresses each standard and also identifies which sections of each of the Ready, Set, Go problem sets in each lesson are aligned to which standards.

• At the course level, the Course Overview documents make general references to standards that are covered in the course and the units in which those standards will be covered. For example, the Course Overview for Math 2 explains how “[t]he major purpose of Math 2 is to  extend the mathematics that students learned in Math 1, including working with quadratic, piecewise and absolute value functions, using rigid transformations and triangle congruence criteria to prove geometric relationships, examining the geometry of circles, and using conditional probability to make and evaluate decisions.” Later in the Course Overview, the connection between Math 1, Units 1-3, and Math 2, Units 1-4, is described and then connected to the work with functions in Math 3.

• The Unit Overview in each unit provides information about prior knowledge and where it was addressed. For example, the Unit Overview for Math 3, Unit 3, begins by identifying that the work with higher order polynomials in Math 3 connects to students’ understanding of linear and quadratic functions in Math 1 and Math 2. Towards the end of the overview, connections are made to Math 3, Units 4 and 8.

The materials clearly indicate how individual lessons or activities throughout the series are correlated to the CCSSM. Each lesson identifies the mathematical content standards as well as the relevant Standards for Mathematical Practice (SMP). Examples include:

• In Math 1, Lesson 6.3, the materials identify Focus Standards G-CO.4 and G-CO.5 and Supporting Standards G-CO.1, G-CO.2, and G-CO.6. The lesson also identifies MPs 3 and 7. The Exit Ticket identifies G-CO.4 as the standard to which the lesson should build.

• In Math 2, Lesson 9.6, the materials identify Focus Standard G-GPE.2. The lesson also identifies MPs 3, 7, and 8. The Exit Ticket is also aligned to the Focus Standard for the lesson.

### Indicator 3d

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series provide some strategies for informing all stakeholders, including students, parents, or caregivers, about the program and suggestions for how they can help support student progress and achievement.

Information regarding the mathematics that students will learn is provided in the course and unit overviews for teachers, and the Course Guide provides the following description of the Lesson Summaries, “This section provides the class with a summary of the main mathematical points of a lesson, in student-friendly language. The summary is meant for students to read on their own time, or to help catch them up on a day they were absent. It may also be useful for families who want to understand in more detail what their student is learning. Lesson Summaries are included in the student-facing material.”

Also, the materials include Guidance on School to Home Connections, which provides specific ways educators can share, communicate, and explain the mathematics learned in the lessons at school with parents or caregivers.

### Indicator 3e

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

The Open Up Math HS Course Guide provides detailed information regarding instructional approaches and research-based strategies used throughout the program. It begins with a discussion of the Comprehensive Mathematics Instructional Framework (CMI) stating “The CMI framework developed by the BYU-Cites public school partnership provides access to research-based principles and practices of teaching mathematics through problem solving and inquiry. This framework includes a teaching cycle and learning cycle connected within a continuum of mathematical understanding. The CMI Framework focuses task instructional implementation on the future—where the learning can go—through what is referred to as The Teaching Cycle. Also within the framework is careful attention to The Learning Cycle continuum of conceptual, procedural, and representational. By using the Teaching Cycle, teachers guide students through the Learning Cycle in order to help them progress along the Continuum of Mathematical Understanding.” Also included in the Course Guide are explanations of instructional routines and Mathematical Language Routines (MLR) used throughout the series.

In each Teacher Lesson, specific information about how to employ various routines and strategies is provided. For example, in Math 1, Lesson 5.4, in the Launch Narrative, specific guidance is provided around Speaking: MLR 8 Discussion Supports. The guidance suggests that some students might benefit from sentence frames to prompt their thinking or support their thinking. These suggestions are specific to the lesson context. Any lesson throughout the series that includes a routine or an instructional routine will have explanations specific to the lesson in addition to the general explanations provided in the Course Guide. In Math 2, Lesson 6.3, as part of the Launch Narrative, the routine “Pause and Record” is described in the lesson context to help teachers understand how to implement the routine specifically for this lesson.

### Indicator 3f

Materials provide a comprehensive list of supplies needed to support instructional activities.

1/1
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

Course documents provide an Integrated Materials List which lists all materials needed separated by course. In the unit overviews, information about digital tools and other materials that will be helpful for certain lessons are provided at the end of each overview. Each lesson also provides a list of materials needed specifically for that lesson.

### Indicator 3g

This is not an assessed indicator in Mathematics.

### Indicator 3h

This is not an assessed indicator in Mathematics.

### Criterion 3i - 3l

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

8/10
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series partially meet expectations for Assessment. The materials include assessment information that indicates which standards are assessed and provide assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices. The materials partially provide multiple opportunities throughout the courses to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

### Indicator 3i

Assessment information is included in the materials to indicate which standards are assessed.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for having assessment information included in the materials to indicate which standards are assessed.

The materials include multiple formal assessments for each unit including Self Assessments, Quick Quizzes, Unit Tests, and Performance Assessments. Formative assessments at the lesson level include Exit Tickets. Examples of how the content standards are consistently identified for all assessments, except Self Assessments, include:

• At the end of each Quick Quiz, there is a list of standards aligned to each item in the quiz. For example, in Math 1, Unit 9, the Quick Quiz for Lessons 9.1-9.5 lists the standards by item 1. S-ID.6, 2. S-ID.8, 3. S-ID.7, 4. S-ID.6a, 5. S-ID.6a, 6. S-ID.8, and 7. S-ID.9.

• At the end of each Unit Test, a list of standards aligned to each item is provided. For example, in Math 2, the Unit 10 Test identifies that question 9 aligns to three different content standards: S-CP.1, S-CP.4, and S-CP.7. All items are listed and have one to three content standards listed for alignment.

• The Teacher Notes of the Performance Assessments contains Core Standards Focus, which lists the standards addressed in the task. For example, in Math 3, Unit 5 Performance Assessment, the Teacher Notes lists G-MG.1-3, G-GMD.4, and G-SRT.9-11 as aligned to the task.

• The Exit Tickets included for each lesson identify Focus Standards which are addressed in the problem(s). For example, in Math 1, Lesson 5.3, the Exit Ticket is aligned to A-REI.12 as the Focus Standard.

Examples of the materials identifying the Standards for Mathematical Practice (MPs) in many of the Performance Assessments include:

• In Math 1, Unit 3, the Performance Assessment is aligned to F-IF.1-5 and MPs 1, 2, 3, 6, and 8.

• In Math 2, Unit 3, Performance Assessment, the Teacher Notes identify content standards A-SSE.3, A-REI.4, and F-IF.8 and MP7.

• In Math 3, the Unit 6 Performance Assessment aligns to F-TF.5 and MP4.

### Indicator 3j

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

2/4
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series partially meet expectations for including an assessment system that provides multiple opportunities throughout the series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. Specifically, the assessment system provides multiple opportunities to determine students' learning and suggestions to teachers for following-up with students but does not provide sufficient guidance for interpreting student performance.

Answer keys with possible solutions are provided for Quick Quizzes, Unit Tests, and Performance Assessments. There are statements which identify possible misconceptions and student understandings provided in the assessments. There are no rubrics provided for constructed-response questions as indicated in the Open Up HS Math Course Guide. The Performance Assessments include Evaluation of Understanding tables, but these tables do not provide tiered criteria or scores, in turn providing little to no guidance to interpret student understanding. With the lack of scoring criteria for the assessments provided, there is not sufficient guidance to fully interpret student performance.

Overall, the materials provide Evidence of Understanding and Evidence of Misconceptions in multiple places throughout the series. However, the evidence provided is not sufficient to interpret student performance overall. Examples of where the materials identify possible student understandings and misconceptions include:

• In Math 1, Unit 5 Test, Problem 9, students explain how they know how many solutions a system of equations will have. Possible explanations are provided along with statements identifying Evidence of Understanding and Evidence of Misconception. Evidence of Understanding for this problem includes “Correct descriptions or examples of how one solution, no solution or infinitely many solutions will look on a graph” and “Correct descriptions or examples of how one solution, no solution or infinitely many solutions are identified when solving with algebraic methods such as substitution or elimination.”

• In Math 2, Unit 6, the Performance Assessment provides an Evidence of Understanding Table that provides Indicators of Understanding and Indicators of Misconception for each problem. For problems 3 and 4 in the task, the Indicators of Misconception include “Does not know to divide the distance traveled by the swim rate” and “Misuses or ignores the units when dividing (no dimensional analysis).”

• In Math 3, Unit 2, Quick Quiz 2.3-2.5 provides an answer key for each problem. The quiz begins by identifying two major misconceptions around properties of logarithms. The narrative provided for teachers states “A common misconception when using the three properties of logarithms is to apply the rule but omit writing ‘log’ next to the term. An expected response for question 1 might be $$\log_2(3x^2)=2\log_2(3+x)$$ or for question 2: $$\log_5(\frac {x} {x+2})=\log_5(x)-(x+2)$$. These two answers indicate a partial understanding of the property, but they are incorrect. Placing the 2 in front of $$\log_2(x+3)$$ is also an incorrect use of the exponent rule.”

Examples of guidance to respond to student needs elicited by the assessment include:

• In Math 2, Unit 5 Test, Question 4, students complete the statement provided by filling in the blanks with words and/or phrases that make the statement true. The notes provided for teachers state “Students that are not able to correctly fill in the blanks may be lacking understanding of the attributes of transformations. Students struggling with this question should revisit task 5.5.”

• In Math 3, Unit 5, Quick Quiz 5.5-5.7, Problem 2, students find the measure of the indicated angle. The notes provided for teachers state “Once the length of $$\overline {BC}$$ is determined, there is enough information to implement the Law of Sines. If the student obtains an incorrect value for $$\overline {BC}$$ but uses the value correctly in this question, they have demonstrated understanding. Students who struggle with this question should revisit task 5.7 and the aligned RSG.”

### Indicator 3k

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

4/4
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices across the series.

The materials include an array of assessment types and opportunities to assess student understanding for each unit. Each lesson includes Exit Tickets and Retrieval, Ready, Set, Go problem sets. Each unit includes Self Assessments, Quick Quizzes, a Unit Test, and a Performance Assessment.

Examples of different types of modalities used for student assessments include:

• In Math 1, Unit 6 Test, students graph, express transformations algebraically, and justify their answers. The Unit 6 Performance Assessment provides an example of students playing a game that includes an expectation of precise mathematics (MP6) as well as engagement in math practices by all participants. Specifically, the instructions state, “Following the end of the game, each player needs to write a justification describing how they know each quadrilateral they recorded on their recording sheet is actually a quadrilateral. The recording sheets will be turned in and graded for accuracy and completeness of the justifications. This step needs to be completed by each player, regardless of the number or type of quadrilaterals that were completed during the playing of the game.”

• In Math 2, Unit 9, Performance Assessment, students work individually or in pairs to: write equations of different conic sections given specific information about each, describe the important features of the graphs, sketch the graphs, and find intersections of different graphs. Students prove the points of intersection they have identified are correct for problem 5.

Examples of different types of items used for student assessments and how they are used to measure student performance include:

• In Math 1, Unit 8, Quick Quiz 1 assesses student knowledge of the key features of quadrilaterals and the properties of parallel and perpendicular lines. In problems 1 and 2, students select four points that form a given quadrilateral then prove how they know the chosen points form the given quadrilateral. Problem 3 assesses students’ knowledge of the properties of parallel lines. The notes provided for teachers indicate that students are expected to use slope in their explanation of why the two lines are parallel (MP6).

• In Math 2, Unit 10, Performance Assessment, students analyze the data from a 2-way table, using probability notation, a Venn diagram and a Tree diagram in order to determine if the test is useful to identify whether a patient has the condition. Students must state and justify their conclusion (MP3) based on the data.

Examples of how assessments address complexity include:

• In Math 3, Unit 1 Test, problem 2 states “f(x) and g(x)are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axes. Which of the following would be true?” There are four multiple choice responses offered. While only one is true, the remaining three distractors test the student’s clear understanding of inverse functions and vocabulary related to transformations. If students choose any of the three distractors, the teacher would have additional insight into any misconceptions.

• In Math 2, Unit 3 Test, Problem 2, students write functions in standard form and factored form for functions which are given as graphs (one of the functions has no real solutions). Students utilize MP2 as they shift from a graphical to a symbolic representation of the functions, consider the units involved, and attend to the meanings of the root quantities that must be present in the factored form.

### Indicator 3l

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials do not provide accommodations (e.g. text to speech, increased font size, etc.) that ensure all students can access the assessments. Therefore, the assessments do not include guidance for teachers on the use of provided accommodations.

### Criterion 3m - 3v

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

8/8
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics; extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity; strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning course-level mathematics; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

### Indicator 3m

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics.

The Open Up HS Math Course Guide provides guidance on strategies and accommodations for special populations outlining best practices to support all students, as well as students with disabilities (SWD), English Language Learners, and students in need of enrichment. The Open Up HS Math Course Guide states “The philosophical stance that guided the creation of these materials is the belief that with proper structures, accommodations, and supports, all children can learn mathematics. Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students. While the suggested supports are designed for students with disabilities, they are also appropriate for many students who struggle to access rigorous, course-level content. Teachers should use their professional judgment about which supports to use and when, based on their knowledge of the individual needs of students in their classroom.” Examples of where and how the materials provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations include:

• In Math 1, Lesson 4.6, students solve linear inequalities. The Launch Narrative in the Teacher Notes states “Representation: Language and Symbols: Encourage students to use the Takeaway section of their notebook that contains previously learned facts about inequalities including examples of how to read statements with inequalities correctly (for example, 1>x can be read as “1 is greater than x” or “x is less than 1”). Providing this resource to students can support them in decoding the symbols as well as recalling information from long-term memory. Therefore, students can focus using their short-term memory which is where problem-solving and computation takes place.”

• In Math 1, Lesson 9.2, students solidify understanding of correlation coefficients and develop linear models for data. In Explore, Teacher Notes, the Students with Disabilities (SWD) Support is identified as Action and Expression: Organization; Memory. In the Explore Narrative, this support is explained, and teachers provide students with a graphic organizer to assist students in staying organized and better reflect on the specific task.

• In Math 2, Lesson 2.6, students factor trinomials using rectangular area models and the distributive property. In Explore, Teacher Notes, the SWD Supports are listed as Representation: Visual-Spatial Processing; Attention, Engagement: Attention; Organization; Social-emotional functioning. The listed supports are explained in the Explore Narrative. For Representation, teachers allow students to manipulate algebra tiles or use Desmos to assist students in visualizing a new concept and develop greater understanding. Teachers also encourage students to create the area diagrams without the tiles or technology. The Engagement support suggests students choose two or three problems on which to focus, which can improve task initiation.

• In Math 3, Lesson 8.3, teachers support students with disabilities as students choose the method they find most useful for understanding the graph of a bungee jump (time vs height). The options include a mental model, a graph on paper, or a graph with technology.

### Indicator 3n

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity.

Each course in the series includes Enrichment lessons identified with an “E.” Based on the information provided in the Open Up HS Math Course Guide, these lessons “align primarily with CCSSM (+) standards and/or engage in mathematics that goes beyond the expectations of the standards (^). The content is not required for students to engage in the full set of non-enrichment lessons. Some non-enrichment lessons may include (+) standards and /or (^) if the content is related to the mathematics of the lesson and can be explored simultaneously with the non-plus standards of the lesson. Enrichment opportunities are distributed throughout the curriculum as natural extensions of the mathematics of the units. Consequently, the mathematical ideas of the Enrichment lessons are accessible to all students.” The use of these lessons is left to the discretion of the teacher; the guidance does not indicate whether the lessons should be used for the whole class or for specific groups of students. However, some units that include Extension lessons also include a second copy of the Unit Test which includes additional problems that address the Enrichment lessons. Examples of lessons that enrich and/or extend the learning of the course-level mathematics include:

• In Math 1, Lessons 4.7-4.9, students use matrices as a means to organize and manipulate data. This is the first time students have been introduced to the concept of a matrix. Students build, add, scale and multiply matrices over the three lessons. The data presented for use is very similar to the cafeteria information from previous (non-enrichment) lessons in the Unit. These lessons cover the N-VM.C+ standards. There are two versions of the Unit 4 Test. The Unit 4 Test E includes 8 additional questions (for a total of 18 questions) which align to the standards in Lessons 4.7-4.9.

• In Math 2, Lesson 3.8, students work with complex numbers as points and vectors as they justify operations with complex numbers. Students bring an understanding of a vector from Math 1 and will take the understanding of complex numbers to Math 3 (roots of polynomial functions).

• In Math 3, Unit 4 is focused on rational functions and expressions and addresses F-IF.7d+ and A-APR.7+, along with additional non-plus supporting standards. Each lesson in the unit is labeled as an Enrichment lesson. This unit extends student understanding of polynomials by using them to create rational functions. Students extend transformations from quadratic functions in Math 2 and logarithmic and polynomial functions in Math 3 to rational functions. Finally students develop their own method to solve a rational equation.

Across the series there are problems that require higher levels of complexity and/or extend the mathematics beyond the scope of the standards, these problems are expected of all students. Examples include:

• In Math 2, Lesson 10.4, students calculate probabilities based on data from a two-way table. Students then write and verify conjectures to develop the definition of a conditional probability.

• The Performance Assessments provide opportunities for students to engage in grade-level content at a higher level of complexity as students often explain and/or justify their thinking as part of the solution to the task. For example, in Math 3, Unit 9, Performance Assessment, Problem 6, students use a simulation to see if there is evidence to suggest that athletes from 2012 were faster than normal. There are multiple explanations students can provide to justify their reasoning, and different simulations can provide different data.

• Each lesson provides at least one problem in a section titled Ready for More? which extends the mathematics of the lesson. For example, in Math 1, Lesson 4.6, students practice solving linear inequalities. The Ready for More? extends the mathematics of the lesson when students use reasoning skills to solve two absolute value inequalities. While the Open Up Math HS Materials Guidance indicates that “fast finishers should be encouraged to work on these extensions,” there is no specific guidance around students who demonstrate a need for an extension of the mathematics in the lesson.

### Indicator 3o

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

Narrative Evidence Only
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials provide varied approaches to learning tasks, in how students are able to share their thinking, and in how students are expected to demonstrate their learning, and the materials provide varied opportunities for students to monitor their learning based on feedback from a few sources. There are opportunities for peer feedback through instructional dialogues, but in many cases, the person monitoring student thinking and providing feedback is the teacher during instruction or in response to an assessment.

Examples of varied approaches for students to share their thinking, ask questions, investigate, make sense of phenomena, and problem-solve using a variety of formats and methods include:

• In Math 1, Lesson 5.4, students examine the methods Carlos and Carlita used to write equations for the constraints provided. Students work individually to rewrite the equations from standard form to slope-intercept form (and vice versa). Students work in pairs to complete the task and share their work with the whole class.

• In Math 2, Lesson 6.5, students apply geometric theorems in computational work, such as finding the missing sides in right triangles using the Pythagorean Theorem. In Jump Start, students make a conjecture about the relationship between the number of sides in a polygon and the number of diagonals that can be drawn from any one vertex of the polygon. Students work independently at first, then discuss their conjectures as a class. In Explore, students work individually for 10 minutes to find as many of the missing measures in the diagram as they can. Students are put into pairs to compare, discuss, and complete the task. Question 5 is worded in such a way as to allow for both deductive and inductive reasoning. The class as a whole discusses possible conjectures and each pair defends the conjecture they wrote to the class.

• In Math 3, Lesson 8.3, students write equations for a given graph and share their equations with the whole class. Students work with partners to try to build a model to represent the height and distance of a bungee jumper using graphing calculators. Students choose appropriate functions, decide how to combine the functions, and adjust the parameters until the model fits. The Teacher Notes indicate that Guess and Check is an appropriate strategy for this task. Students follow the same process on another modeling problem in Explore.

The materials give students opportunities to monitor their own progress and learning through ongoing review, practice, and self-reflection, and feedback is primarily provided by the teacher. Examples include:

• Each lesson has a set of practice exercises titled Retrieval Ready, Set, Go. The Retrieval exercises are aligned to the Ready and Go sections. Guidance is provided for the Retrieval exercises which indicates how the items connect to upcoming work or to work previously completed. The Ready exercises review skills needed for upcoming lessons in the current unit or future units. The Set exercises focus on the material addressed in the current lesson. The Go exercises remind students of mathematics learned earlier in the unit, previously in the course, or in previous math courses.

• Exit Tickets, Performance Assessments, and Quick Quizzes present opportunities for students to monitor their learning, and in each instance, the teacher is the primary source of any feedback.

• Students have an opportunity in each unit to complete at least one Self Assessment based on a set of lessons from the unit. On each Self Assessment, “I can” statements are provided for students to reflect upon after the lessons are complete. Students select one of the following levels of understanding for each “I Can” statement: “I can understand and do it without any mistakes;” “I understand most of the time, but I’m still working on it;” and, “I don’t understand this yet.”

### Indicator 3p

Materials provide opportunities for teachers to use a variety of grouping strategies.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series provide opportunities for teachers to use a variety of grouping strategies. Notes for the teacher indicate what types of groupings can be used for the activities. Throughout the series, generally lessons have students work on a task individually to start, then share their work with a partner or small groups, which is followed by a whole group discussion.  Explanations of the grouping strategies do not provide guidance around how the grouping strategies differ based on needs of students. Examples include:

• In Math 1, Lesson 6.2, Launch, students use a Think-Pair-Share routine to connect previous learning about perpendicular lines to new learning about transformations. In Explore, students work individually to rotate a triangle. Then they work in pairs to compare their images and develop conjectures and justifications for the slope of perpendicular lines.

• In Math 2, Lesson 10.5, Explore, students work on the first two problems individually finding probabilities from data presented in a two-way table and answering questions about those probabilities. Then students share their work with a partner, and they complete the task either in pairs or in small groups. In Discuss, the teacher leads a whole-group discussion by selecting students to share their probabilities for different questions. Guidance directs teachers to use this discussion time as an opportunity to clarify misconceptions around conditional probabilities and independence.

• In Math 3, Lesson 6.5, Jump Start, students work individually to identify three things they notice about a given graph of a Ferris wheel ride. Then students share their writing with a partner. The Launch portion of the lesson is presented to the whole group. In Explore, students work individually on the first two problems, then they share their graphs with a partner. During Pause and Reflect, students reflect on questions presented by the teacher and share their thoughts with a partner or small group. In Discuss, students define the cosine function during a whole group discussion.

### Indicator 3q

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

2/2
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The Open Up HS Math Course Guide includes a section titled Supporting English Language Learners which states “Embedded within the curriculum are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012). Therefore, while these instructional supports and practices can and should be used to support all students learning mathematics, they are crucial to meeting the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English.”

The Course Guide also indicates that the implementation of Mathematical Language Routines (MLRs) will support ELL students. The Course Guide states “The mathematical language routines (MLRs) were selected because they are effective and practical for simultaneously learning mathematical practices, content, and language. A mathematical language routine is a structured but adaptable format for amplifying, assessing, and developing students' language.” The eight MLRs included in the materials are: MLR1 Stronger and Clearer Each Time; MLR2 Collect and Display; MLR3 Clarify, Critique, Correct; MLR4 Information Gap; MLR5 Co-Craft Questions and Problems; MLR6 Three Reads; MLR7 Compare and Connect; and MLR8 Discussion Supports.

Examples of the materials utilizing the MLRs and additional supports for EL students based on the language demands of the lesson and examples of appropriate support and accommodations for EL students that will support their regular and active participation in learning mathematics include:

• In Math 1, Lesson 2.1, there are two opportunities for students to Pause and Record, which is an intentional break in the lesson where students record insights from the teacher to formalize concepts and describe it with the appropriate vocabulary and notation in order to develop their vocabulary and knowledge of mathematical concepts. During the Discuss portion of the lesson, students first Pause and Record vocabulary around the domain of a function and arithmetic sequences. The second opportunity for Pause and Record allows students to record takeaways from the lesson concerning geometric sequences, and discrete and continuous functions.

• In Math 1, Lesson 6.2, the Launch Narrative describes MLR2 Collect and Display. Teachers circulate throughout the classroom listening to students’ discussions and recording key words and/or phrases related to justifying whether lines are parallel. The words and/or phrases are then displayed for the class so students can refer to, build on, or make connections with the concepts during future discussions.

• In Math 2, Lesson 5.2, MLR 8 Discussion Supports is utilized. Teachers provide sentence frames for students to prompt their thinking or provide support to explain their thinking. After students have time to develop their thoughts, they share their thoughts with a partner rehearsing what they will share with the whole group. Rehearsing allows students to clarify their thinking further.

• In Math 2, Lesson 10.2, the Launch narrative describes MLR5 Co-Craft Questions. Teachers present a scenario with data without presenting the problems from the lesson. Students then craft one or two mathematical questions that could be asked about the data provided. Students share their questions with partners. Some students share their questions with the class. This allows students to spend some additional time making sense of the data provided and understanding what information is missing which will, in turn, increase their ability to answer the questions posed in the lesson.

• In Math 3, Lesson 1.3, the Launch Narrative describes MLR6 Three Reads. Students will read the scenario, including problems 1 and 2, three times. The first read is to be able to tell the story without mathematical details. The second read is to find the mathematical details (both what they know and what they want to know). The third read is to find an idea on how to get started with solving the problems. This can help students make sense of the problem and decipher language as they discuss the scenarios with partners after each read.

• In Math 3, Lesson 9.11, students use MLR1 Stronger and Clearer Each Time. Students develop a written first draft as a response to a prompt, meet with two to three partners where each partner gets a turn to be a speaker and listener, and students write a second draft of their response revising their thinking based on the conversations with their partners. Students defend their position on whether the data presented provides evidence that students perform better on tests when listening to music.

### Indicator 3r

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series provide a balance of  information about people, representing various demographic and physical characteristics. Across the series, the materials have few images of people. Most images of people are included in the assessments. The few images do provide a balance between male, female, and other characteristics.

Although the names used in the lessons are not associated with pictures, the names used across the series provide a balance between male, female, and other characteristics. Examples include:

• In Math 1, Unit 5 introduces the Martinez twins, Carlos and Clarita, and their plan to open a pet sitting business to make money during summer vacation. Every lesson in the unit mentions Carlos and Carlita as they deal with different aspects of their business. In Lesson 5.5, Ready for More?, Carlos has twisted his ankle which affects the time he spent caring for the pets. In Lesson 5.7, Explore, Problem 5, Amanda critiques Frank’s work, and the lesson further explores Carlos and Clarita’s pet sitting business. In Lesson 5.10. Explore introduces three of Carols and Carlita’s friends, Stan, Jan, and Fran, who are purchasing school supplies.

• In Math 2, Lessons 10.3 and 10.5, Freddy owns Fried Freddy’s and his friend Tyrell, a business friend, helps him to analyze data from his restaurant.

• In Math 3, Lesson 5.4, Tatiana is helping her father purchase supplies for a deck he is building.

### Indicator 3s

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do not provide guidance to encourage teachers to draw upon student home language to facilitate learning. ELL students are supported by the regular use of Math Language Routines, but these supports are for the student to understand the math and to do so in English rather than in their native language. These resources are used to help all students understand the math regardless of any language barriers.

### Indicator 3t

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. No references to cultural or social supports to facilitate learning were found.

### Indicator 3u

Materials provide supports for different reading levels to ensure accessibility for students.

Narrative Evidence Only
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do provide some supports for different reading levels to ensure accessibility for students.

Examples of strategies to engage students in reading and accessing grade-level mathematics include:

• In Math 1, Lesson 9.7, the teacher notes include emphasis for teachers to work with students on using appropriate vocabulary as students justify their choice of a bridge design based on distributions of the weights different designs have held. Students make a variety of different arguments and present their choice in their own words. Teachers then encourage students to use more formal terminology. Teachers are also guided to facilitate a conversation to get students to talk about the analysis involved and to repeat students’ statements using formal terminology.

• In Math 2, Lesson 10.4, students create and analyze attributes of Venn diagrams and make sense of data. Students engage in MP1 by making sense of probability notation and new vocabulary (mutually exclusive, joint, and disjoint) in context. Students also engage in MP6 by using precise vocabulary and computation, especially as students work to connect the concepts of the unit to the visual representation of a Venn diagram.

• The instructions for the launch of the Math 3, Unit 4, Performance Assessment state “Begin the task by reading the scenario and ensuring students understand that there are two hoses working together.” The launch instructions go on to allow time for the students to grapple with the concept and develop an understanding of how best to describe the rate in terms of number of pools and minutes. The final sentence in the teacher instructions for the launch states “As students work, provide support for students who are having difficulty in reading and understanding the prompts.” However, no examples of strategies or supports are provided.

• Math Language Routine 6, “Three Reads” supports reading comprehension, sense-making, and meta-awareness of the mathematical language as well as negotiating information in a text with a partner through mathematical conversation. This routine is used in Math 3, Lesson 6.1 as students unpack the mathematics of the Ferris wheel model.

The materials provide multiple entry points that present a variety of representations to help struggling readers access and engage in course-level mathematics. Examples include:

• In the Teacher Notes, Monitor Student Thinking, there is often a sentence that starts, “For students who don’t know where to begin…” followed by a suggestion for how to get them started. For example, in Math 1, Lesson 5.2, the suggestion is for students to assume that Carlos and Clarita follow the father’s advice and calculate the income with the same number of cats and dogs. These suggestions serve to provide multiple entry levels.

• In Math 2, Lesson 5.7, students write proofs to show that conjectures they have developed are always true. The Explore Narrative in the Teacher Notes states “There are a variety of ways students can approach the proofs of these theorems, both in terms of the conceptual approaches they use (transformations, linear pairs, congruent triangle criteria) and in terms of the format they use to write their proofs (two-column, flow diagrams, narrative paragraphs, algebraic proof).”

• In Math 3, Lesson 1.3, Retrieval Ready, Set, Go, Problems 7-15, students read a short story about Jack and the Beanstalk and answer questions about the exponential model that Jack uses to calculate the height of his beanstalk as a function of time. Students have multiple entry points to these problems because the information is provided through multiple representations: the verbal information presented in the story is accompanied by a table of values (time in hours versus height in feet) and a function expressed symbolically.

### Indicator 3v

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series uses physical and/or virtual manipulatives to help students develop understanding of mathematical concepts. Some manipulatives---such as colored pencils, scientific calculators, and Desmos---are used routinely by students at their discretion to support their learning and explain their understanding. Examples of the manipulatives and how they are used to help students develop understanding of a concept include:

• In Math 1, Lesson 1.1, students use colored pencils to shade cubes in ways that represent sequences. In Lesson 4.8E, students use colored pencils or markers to highlight how the elements from each of the matrices connect in matrix multiplication.

• In Math 1, Unit 6, each lesson uses a physical or virtual manipulative. In Lessons 6.1-6.6, Black Line Masters (BLMs) support students as they develop definitions of geometric transformations, use geometric descriptions to transform figures, and specify sequences of transformations that map one figure onto another.

• In Math 2, Lesson 6.1, students use a rubber band stretcher to develop the concept of dilations. There is also a GeoGebra app provided that replicates the activity.

• The materials list for Math 2, Lesson 8.8 indicates two GeoGebra apps that are intended to support students develop their conceptual understanding of Cavalieri’s Principle.

• In Math 3, Lesson 5.1 recommends a host of manipulatives to assist students as they explore cross sections of 3-D geometric solids. The materials list includes play-doh and dental floss for slicing solids, transparent 3-D figures to which water can be added, a sealed jar containing a colored liquid that can be tilted to illustrate possible cross sections, and flashlights for creating shadows of objects.

• In Math 3, Lesson 7.4, an alternative graphing activity is provided for Explore question 4, where students cut varying lengths of spaghetti to represent line segments for specific angles of rotation, then glue those pieces to a large graph. This allows students to create a physical model of the line segment used to represent the value of the tangent for a particular angle of rotation.

• In Math 3, Lesson 7.8E, the BLMs include images of the polar and coordinate planes as well as location and angle specification cards to help students as they engage with proofs and applications of trigonometric identities.

• In Math 3, Lesson 9.9, Launch, students find a margin of error and a plausible interval for a sample proportion using a simulation where student pairs are given a bag of dark and light colored beans representing artifacts more than 1000 years old and artifacts less than 1000 years old, respectively. Using physical manipulatives for this simulation helps students develop conceptual understanding around creating an interval that is likely to include the population proportion.

Examples of how manipulatives are connected to written methods include:

• In Math 1, Lesson 1.1, students “draw multiple diagrams with the checkerboard pattern such as a 3 ⨉ 3, 4 ⨉ 4, 7 ⨉ 7, etc., or use manipulatives to see patterns as the checkerboard increases or decreases.” Students then turn to a partner to use the following prompt to explain what they notice about the pattern: “When I looked at the diagram, I noticed _________________ and so I ____________________.” Students then “create numeric expressions that exemplify their process and require students to connect their thinking to the visual representation of the tiles.”

• As part of the alternative graphing activity in Math 3, Lesson 7.4, Explore task, question 4, students draw the unit circle on a large sheet of paper so that they can indicate how the line segment is defined in that context as well. The activity then allows students to practice using appropriate tools strategically (MP 5) by prompting them to refer back to their unit circle using sentence frames such as: “I used the unit circle as a tool to think about ____ by ____,” and “I used the unit circle to calculate ____.”

### Criterion 3w - 3z

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

0/0
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in course-level standards. The materials do not include or reference digital technology that provides opportunities for collaboration among teachers and/or students. The materials have a visual design that supports students in engaging thoughtfully with the subject, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

### Indicator 3w

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

Examples of the materials providing digital technology and interactive tools for students include:

• In Math 1, Unit 5 includes two specific GeoGebra apps for engaging students. In Lesson 5.3, students enter the parameters of constraints and a specific number of cats and dogs that are appropriately color-coded to signify “too big,” “not too big,” or “just right” for the constraint. The app provides feedback by plotting points in black if students predict the meaning of the point incorrectly (A-CED.2, A-REI.12, MPs 2 and 7). In Lesson 5.6, students interact similarly with another specifically designed GeoGebra app to examine the solution set for a system of linear inequalities. (A-CED.3, A-REI.12, MPs4 and 7)

• In Math 2, Lesson 6.2, students work with rubber band stretchers to dilate triangles. There is a GeoGebra app included that allows students to investigate rubber band stretchers digitally/virtually. The teacher notes do not specify when or how this app should be used. Little direction on how to navigate the app is provided.

• In Math 3, Lesson 5.1, students visualize cross sections using digital drawing apps. Cross sections can be visualized by connecting points on the edges of 2-D drawings of the 3-D shape to form a region that lines in a plane. (G-GMD.4, MP7)

• In Math 3, Lesson 7.3, a GeoGebra app supports students’ engagement by helping students visualize a Ferris wheel and the position of the rider. Students can toggle different settings such as the height, radius, and period; make predictions about the shape of the graph of the height of the rider as a function of time; and then play the simulation to check if their predictions were correct. The accompanying teacher notes explain that “technology tools can eliminate barriers and allow students to more successfully take part in their learning” and that it provides support for conceptual processing. (F-TF.5, F-BF.3, MP2)

When links to the apps are included there is little guidance for the teacher or students about how to use the apps. Also the apps are not included in the student materials; they are included only in the Teacher Notes. There is no evidence of digital materials that can be customized to attend to student and/or community interest.

### Indicator 3x

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series do not include or reference digital technology that provides opportunities for collaboration among teachers and/or students. No evidence of opportunities for collaboration among students, between the teacher and the student, or among teachers was found in the materials.

### Indicator 3y

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials use a consistent layout and structure across units and lessons. As described in the Course Guide, “Each unit follows an instructional framework that builds from a Develop Understanding lesson to one or more Solidify Understanding lessons to one or more Practice Understanding lessons. This framework remains consistent across units and within units that have more than one cycle.” Each lesson includes Learning Goals, Standards for the Lesson, Required Preparation, Progression of Learning, and Purpose as background for the teacher. The teaching cycle then follows the Launch, Explore, Discuss sequence. Some lessons also include a Jump Start prior to the Launch.

The materials include images, graphics, and models that support student learning and engagement without being visually distracting. Examples include:

• In Math 1, Lesson 9.1, the student learning focus is on representing data using a scatter plot, understanding the meaning of the correlation coefficient, and describing the difference between correlation and causation. The materials provide seven sets of cards that contain tables of data and scatter plots of the data. Students examine the data and put the cards in a justifiable order. In addition, students compare each scatter plot with its correlation coefficient and describe patterns.

• In Math 2, Lesson 6.1, students investigate dilations. The provided BLM includes the original image and a portion of the dilated image. Students use the BLM to determine where the original picture should have been placed to have the dilated image centered on the page and whether the scale factor used was correct. The image is simple and not distracting.

• In Math 3, Lesson 5.3 addresses estimation of volume based on a two-dimensional cross-section. Students develop or present a strategy for estimating the volume. The graph of the trapezoid and the two-dimensional representation of a vase are not visually distracting or confusing to students.

• In Math 3, Lesson 8.4, Explore, Problem 10 provides students with a diagram to support their thinking about how the notation and table formats used in previous problems might be combined. The image is simple with arrows showing the direction of the function sequence from one component to the next, in the order in which the components are combined. This image for function composition is then revisited in the Launch task of Lesson 8.5, where students use a “starter set” of functions to build composite functions, filling in the diagram to show how their function can be decomposed into its component parts.

Examples of images, graphics, and models that clearly communicate information or support student understanding of topics, texts, or concepts include:

• In Math 2, Unit 8, Performance Assessment, students consider how someone might build a clay model of the Leaning Tower of Pisa. The materials provide students with a picture of the tower as well as a description of the tower’s various shapes/dimensions. While this is only a picture of the actual tower, it provides a valuable reference for students who may not be familiar with the Tower.

• In Math 2, Lesson 3.8E, Jump Start, the materials provide students with a coordinate plane diagram and a series of questions intended to activate their background knowledge of vectors from a previous course. The inclusion of this type of diagram helps to model computations with complex numbers as students are able to see both the arithmetic and geometric perspective represented.

• In Math 3, Lesson 5.4, an image of the nails needed to complete the deck is provided. Students use this drawing on the coordinate plane to find the volume of the nail in order to calculate the cost of the deck. The image clearly identifies the points students can use to determine the lengths. The axes are precisely labeled to represent tenths of an inch.

### Indicator 3z

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Integrated series provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

Examples of guidance for using embedded technology to support and enhance student learning, where applicable, include:

• In Math 1, Lesson 5.3, the following guidance on how to use the embedded GeoGebra resource was provided to teachers within the teacher notes: “A GeoGebra app has been designed specifically for this task, and can be found here: https://www.geogebra.org/m/FWe7PzOO.  The app allows students to make the same mathematical decisions as described in the task below, including deciding what color to make each plotted point: the “too big” color red, the “not too big” color orange, and the “just right” color green. The app provides feedback by plotting points in black if students predict the meaning of the point incorrectly.”  In addition, the materials indicate “Provide access to the GeoGebra app as described. Technology tools can eliminate barriers and allow students to more successfully take part in their learning. Students may need direct instruction in how to access these tech tools and may benefit from a list of steps to be able to use the applet or software.” The direct instruction mentioned is not provided for teachers to be able to give to the students.

• Across the series, the materials often suggest the use of dynamic Geometry software without specific teacher guidance. In Math 1, Lesson 7.1 is an exception, however, where the materials advise the teacher to “restrict students to using the circle-by-measure and line tools.”

• In Math 3, Lesson 7.4, Launch, students visualize the graph of a tangent function using a line segment drawn tangent to the unit circle at the point (1, 0). The length of this segment changes as the angle of rotation θ changes, allowing students to visualize the magnitude of the tangent value for different angles of rotation by examining the length of this segment. In Explore, the materials provide guidance to teachers about using technology to assist with this visualization. The guidance directs teachers to find an external resource without any specificity of which “video or technology activity” would best support students’ engagement with this concept: “Connecting the tangent line on a circle diagram to the graph of a tangent function will deepen student’s understanding of the tangent function and prepare them to interpret and utilize the graph for solving problems. Find a video or technology activity that demonstrates finding the various lengths of tangent lines for angles of rotations and uses those to create the graph (or use the alternate graphing method mentioned in the teacher notes). Visualizing the creation of the tangent graph will assist in developing conceptual understanding.”

abc123

Report Published Date: 2021/06/09

Report Edition: 2021

Title ISBN Edition Publisher Year
Open Up Resources HS Mathematics Math I Student Course 9781953454874 Open Up Resources 2021
Open Up Resources HS Mathematics Math I Teacher Course 9781953454881 Open Up Resources 2021
Open Up Resources HS Mathematics Math II Student Course 9781953454898 Open Up Resources 2021
Open Up Resources HS Mathematics Math II Teacher Course 9781953454904 Open Up Resources 2021
Open Up Resources HS Mathematics Math III Student Course 9781953454911 Open Up Resources 2021
Open Up Resources HS Mathematics Math III Teacher Course 9781953454928 Open Up Resources 2021

## Math High School Review Tool

The high school review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The High School Evidence Guides complement the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.