The instructional materials reviewed partially meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. In general, the series included the majority of all of the non-plus standards, but there were some instances where the full intent of the standard was not met.

Below are the non-plus standards that were not fully addressed and descriptions of how they were not fully addressed:

• A-SSE.1: Students are often shown how the information from a context is related to an equation or expression, yet evidence was not found where students interpret expressions in terms of the represented context. The materials regularly highlight and provide nomenclature for the parts of expressions, yet students are not required to interpret the parts of the expression in terms of the context. For example, Lesson 4-7 of Algebra 1 highlights the first term, term number, and common difference in arithmetic equations. In these cases, students are regularly shown the parts of an expression in order to replicate an example without needing to interpret the parts of an expression in terms of the context the expression represents. Furthermore, the materials focus on words within the standard (like “factors”) without requiring students to interpret the structure. For example, the cumulative review in the TE on page 610 in Algebra 1 asks students to “Factor the expression 3x^2 + 23x + 14” as the single task aligned with A-SSE.1a. This example is representative of the focus of the materials on words like “factors” within the standard without attending to the requirement for students to interpret expressions in terms of their context.
• A-SSE.3: Students regularly factor and complete the square throughout the series, yet the standard requires students to “Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.” Evidence was not found that the materials require students to choose a form in order to reveal information. For example, the Algebra 1 TE on page 576 directs students to factor to find zeros. Similarly, students are directed to “solve by factoring” in the Algebra 1 TE on page 571 and “Find the vertex of each parabola by completing the square” on page 579 of the Algebra 1 TE. The standard requires students choose and produce an equivalent form in order to reveal information, but the materials regularly direct students which form they should use.
• A-APR.3: Although students graph functions to find solutions to equations (e.g., 3x2 – 12 = 0, Algebra 1 TE on page 564 and x2 – 11x + 24 = 0, Algebra 2 TE on page 229), evidence was not found where students identify zeros of polynomials by factoring and then use the zeros to construct a rough graph of the function defined by the polynomial.
• A-APR.6: No evidence was found where students rewrite a rational expression, a(x)/b(x), in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials.
• A-REI.1: Throughout Algebra 1 and Algebra 2, students solve equations. The examples provided (e.g., problem 3 on page 111 in the Algebra 1 TE) detail the operations, formulas, and properties used in order to solve the equation. Examples like these regularly provide students with sample justifications that "explain each step in solving a simple equation," yet students themselves are not required to explain their steps in solving simple equations.
• A-REI.5: The textbook provides reasoning as to why the “elimination method” works (Algebra 1, Lesson 6.3), yet students are not required to prove that replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as required by the standard.
• A-REI.11: Evidence was not found where students explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Students regularly follow a prescribed method for solving equations. For example, page 596 of the Algebra 1 TE states “Step 1: Graph both equations in the same coordinate plane. Step 2: Identify the point(s) of intersection, if any. The points are (-2,4) and (2,0). The solutions of the system are (-2,4) and (2,0).” Similarly, the Concept Byte on pages 260-261 for Lesson 4-4 of the Algebra 1 TE provides a prescriptive method to solve equations like -4 = -3t + 2.
• F-LE.3: Evidence was not found where students use graphs and tables to observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Students look at rates of change of various function types (e.g., on page 559, Algebra 1 TE), yet they are not required to observe exponential functions overtaking others in these situations.
• G-CO.13: Students construct squares given a side length (in the Geometry TE on page 187), equilateral triangles (in the Geometry TE on page 255), and circumscribed polygons. However, no evidence was found that students construct an equilateral triangle, a square, or a regular hexagon inscribed in a circle.
• G-MG.3: Evidence was not found that students would apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
• S-ID.3: The materials require students to recall definitions as well as calculate measures of center and spread (e.g., Lesson 12-3 in Algebra 1). However, no evidence was found where students are required to interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
• S-ID.8: The materials require students to compute correlation coefficients of a linear fit with technology (on page 339 of the Algebra 1 TE), yet no evidence was found were students interpret the meaning of the correlation coefficient.

Many standards are addressed fully only with the incorporation of the teacher notes and features such as “Concept-Bytes” which are not present in the student materials.

Below are examples of how standards and clusters were fully addressed in the materials:

• N-RN.2: Lesson 6.4 of Algebra 2 includes work specifically around rewriting expressions involving radicals and rational exponents using the properties of exponents.
• A-CED.A: The materials attend to the entirety of this cluster. Throughout the series, students create equations to describe relationships. Students begin writing simple linear equations in the first chapter of Algebra 1, and as the series progresses, students write equations with various functions. Students also create equations to highlight quantities of interest throughout the series, in particular in Algebra 1 and Algebra 2.
• F-IF.2: The series regularly uses function notation and expects students to evaluate inputs for various function types. Additionally, students are required to interpret statements that use function notation in terms of a context (Algebra 1, Lesson 4-6).
• G-CO.C: The entirety of this cluster is fully addressed in the materials. Throughout the geometry course, students prove various theorems about lines, angles, triangles, and parallelograms.
• S-CP.6: In lesson 13-6 of Geometry and lesson 11-4 of Algebra 2, students find conditional probabilities by using the fractional part of desired outcomes that belong to the restrictive event.

The materials partially meet the expectation for, when used as designed, allowing students to fully learn each standard.The following are some examples of how the materials, when used as designed, would not allow students to fully learn each standard. (Those standards that were not attended to by the materials, as noted in indicator 1ai, are not mentioned here.)

• N-RN.1: Students should “Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents…” Lesson 7.2 of Algebra I includes an explanation of this in the Teacher Edition; however, no explanation is noted in the student edition and no indication is noted where students explain. In Lesson 7.3 of Algebra I, there are examples of methods students can use to simplify exponential expressions; however, students are not asked to explain the meaning of rational exponents as the standard requires. Similarly, in lesson 6.4 of Algebra II on page 381, Problem 1 gives an example of this idea; however, students are not asked to explain the meaning of rational exponents.
• F-IF.8b: Students “Use the properties of exponents to interpret expressions for exponential functions.” Lessons 7-3 and 7-4 of Algebra I work with properties of exponential functions. In Example 1B on page 461, students can see the expression 1.07x (in terms of x years) transformed into 1.0057m (a monthly expression); however, no evidence is found where students are interpreting the new expression.That is, students do not have opportunity to fully work with, practice, and learn this standard. Similarly, Lesson 6-8 in Algebra II, page 416, addresses this idea in a “Think Box” near the bottom of the page. Again, no evidence is found where students are interpreting the meaning of the equivalent exponential expression.
• F-IF.9: Students “Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).” The evidence of this standard is found to be very limited. For instance, in Algebra I, three problems are found to address this idea: problem 51 (graph and table) in lesson 5-5 on page 327, problem 40 (table and equation) in lesson 7-6 on page 458, and problems 28 and 29 (equation and table) in lesson 9-2 on page 557. In Algebra II, four additional problems are noted: problem 48 in lesson 2-4 on page 87, problem 43 (equation and table) in lesson 4-2 on page 207, problem 38 (equation and graph) in lesson 5-9 on page 344, and problem 58 in lesson 7-3 on page 457. The limited number of problems provide limited opportunities for students to compare properties of functions represented in different ways, and no evidence is found to support students comparing different functions.
• S-ID.7: Students “Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.” Some discussion of correlation and causation occurs in Algebra I on page 342 in problem 21. While students are given the opportunity to use and determine the slope and intercept, there is no evidence of students being asked to interpret these ideas, either in context or generally.

Opportunities to fully learn the following standards are limited to one Concept-Byte activity.

• G-CO.2: Concept Byte 9-1 in Geometry includes a tracing paper activity, and Concept Byte 9-2 includes paper folding to represent reflections. The online program shows a solution to problems but does not have an interactive program for students to utilize in creating transformations. No evidence is found of students using transparencies to create transformations. Lesson 12-5 in Algebra 2 addresses “geometric transformations” with matrices. While students are given intermittent opportunities to work with transformations, there is no opportunity for students to describe and/or compare transformations which limits their experience and the opportunity to deeply interact with these concepts.
• G-CO.3: Geometry Concept Byte 9-3. pages 568-569, addresses this standard; however, evidence is not found in the student edition asking students to translate a figure back onto itself. In the Teacher Edition, notes include questions that push student thinking to this effect; however, students are not asked to “describe” these things in their problem solving.
• S-ID.5: This standard is addressed in Algebra 1 with Concept Bye 12-5. One more problem was found in Geometry on page 854 with problem 23. This is limited opportunity for students to interact with the topic, understand the use of these tables, and interpret any data revealed within them.
• S-IC.2: The materials state this standard is addressed in Algebra 2 by Concept Byte 11-3. There is material here for probability distributions and cumulative probability in problems 4a,b. Opportunities on this topic are limited and do not allow students to fully understand and interact with the ideas.

The materials partially meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Throughout the series, students engage in age-appropriate situations at a level of complexity suitable for students in this grade span. However, the materials require students to apply only some of the key takeaways from Grades 6-8.

Below are examples of how key takeaways from Grades 6-8 are not applied within the materials:

• Exercises do not regularly require students to perform rational number arithmetic fluently in all the courses. For example, lesson 1-4 in Algebra 2 TE on page 30, “solving equations” provides 23 problems of which only two contain non-integer numbers and only five have non-integer solutions.
• Throughout the materials, students are directed step-by-step to follow a procedure in order to apply key takeaways from Grade 6-8. For example, in Algebra 1 lesson 6-2 TE on page 374, students are given step-by-step instructions showing how to use a system of linear equations to solve a word problem. Rather than "building on students’ previous knowledge and allowing students to make connections to new learning," the materials direct procedures.
• The materials do not require students to apply concepts and skills from 6.SP through 8.SP in their work with high school Statistics and Probability throughout the series. For example, in the last chapter of Algebra 1, students work with histograms and measures of center. The lessons articulate how to create histograms and calculate measures of center without extending the work from 6.SP through 8.SP. Additionally, no evidence was found to support the application of 6.SP through 8.SP concepts and skills earlier in Algebra 1. Similarly, Statistics and Probability is addressed late in Geometry and Algebra 2 with no evidence found for the application of concepts and skills from 6.SP through 8.SP.

Below are examples of how key takeaways from Grades 6-8 are applied within the materials:

• The materials require students to apply ratios and proportional relationships with their work in geometry, namely Chapters 7 and 8 concerning similarity and trigonometry.
• Throughout Algebra 1 and Algebra 2, students apply basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.

The materials partially meet the expectations for fostering coherence through meaningful connections in a single course and throughout the series where appropriate and where required by the Standards. The lessons throughout the Algebra 1 and Algebra 2 materials frequently build mathematically from one lesson to the next, in much the same way as the Geometry materials build from work with area of quadrilaterals and triangles to more diverse polygons and then to circles. However, the materials do not make many connections throughout courses and the series.

The Geometry Progressions for the Common Core State Standards describe a coherent growth in student understanding of congruence founded in rigid transformations in a plane and advocates student use of tools like tracing paper. The progressions go on to state that once a foundational definition of congruence in terms of rigid motion in a plane has been established, “it is possible to transition into the traditional way of proving theorems” (page 13). Instead, the materials move into congruence proofs in traditional format early in the materials (Geometry TE lesson 4-1) where congruence is defined as polygons with congruent corresponding parts. In the Geometry TE lesson 9-1, students are introduced to rigid transformations in the form of translations, reflections, and rotations. In a typical example from the materials, students are asked to combine transformations (Geometry TE on page 601) instead of using those transformations to justify congruence. The task asks students to justify the movement of a puzzle piece onto another without connecting the concept of congruence as the standards require. Likewise, the materials present similarity in Chapter 7 in a traditional manner while redefining similarity in Chapter 9 in terms of transformations without explicitly connecting the previous definition to the new.

The Algebra Progression for the CCSSM describe a tight connection between the work in algebra and the functions domain. Students should see the connection that equivalent expressions are in fact describing the same function, the same relationship between quantities. While the materials define and engage students with equivalent expressions and with functions separately- for example Algebra 1 TE Big Ideas on T26, Algebra 1 TE Math Background on page 613A, Algebra 1 TE Lesson 6-1, and Algebra 2 TE Lesson 3-2- the connection that, for example, equations in a consistent and dependent linear system represent a single function, is absent.

Materials addressing Statistics and Probability occur at the end of each course throughout the series. The treatment of these topics occurs in isolation from the rest of the topics within each of the courses. Additionally, some topics are duplicated in different courses without acknowledging the connections or repetition. For example, Geometry lesson 10-5 and Algebra 2 lesson 14-4 both derive the formula A = 1/2 ab sin(C) for the area of a triangle.

Overall, the series fails to make connections across conceptual categories. Work with the geometry category lives predominantly in the geometry course with minimal connections occurring in the other courses. Conversely, the geometry course is largely devoid of connections to number and quantity, algebra, and functions. Even when connections are being made, or could be made, the materials do not make the connections clear to teachers or students.