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.

The following standards are identified as having been met in this series.

• In Number and Quantity, there was evidence to indicate that the non-plus standards of N-CN were addressed in the Algebra 2 materials. On page 423, the Algebra 1 textbook requires students to pay particular attention to the units of quantities (N-Q.1). Additional items in Activity 33 require students to make choices about the level of accuracy needed in their answers (N-Q.3).
• In the Algebra category, there was evidence to support student engagement with A-APR.A,B and A-REI.A,B. Many opportunities with these clusters were found across both the Algebra 1 and Algebra 2 materials.
• Across the Algebra 1 and Algebra 2 materials, there was evidence to indicate that all aspects of the non-plus standards from the following domains and clusters were addressed: F-IF.B, F-IF.C, F-BF, F-LE.B, F-TF.A and F-TF.B.
• The standards from the Geometry category were predominantly addressed in the Geometry materials, and there was evidence to indicate that all aspects of the non-plus standards from the following domains and clusters were addressed: G-CO; G-GMD; G-SRT.B,C; G-C.B; G-GPE.B; and G-MG.
• In Statistics and Probability, it was determined that all aspects of the non-plus standards were met across the series.

Reviewers did not find evidence of G-SRT.1b anywhere throughout the series. The standard was not identified in the materials.

The following standards are identified as having been partially met in this series in the conceptual categories and domains listed. In general, many of the standards that are partially met earn that classification due to the lack of student opportunity to prove certain aspects stated in the standards.

• N-RN.3: Opportunities to have students explain why the sums/products are rational or irrational are needed. While students have opportunities to predict the outcome of such sums/products (Algebra 1 Activity 20), the explanation of such is not required.
• A-REI.5: While students were given ample opportunities to solve systems via linear combinations, there were no expectations for students to prove that linear combinations worked as a valid method of solution by showing that the sum of one equation and a multiple of the other would produce a system with the same solution.
• A-REI.11: Students are asked to solve systems of equations graphically with a variety of equation types, but they are not asked to explain why the x-coordinates of the points were the solutions to the equation f(x) = g(x).
• F-LE.1a: In Algebra 1, lesson 9-3, students explore the linear aspect but do not explore the exponential aspect of this standard. Also, students are not required to prove that linear functions grow by equal differences over equal intervals nor that exponential functions grow by equal factors over equal intervals.
• G-C.3: Students are given opportunities to construct inscribed and circumscribed circles for a triangle, but they are not asked to prove the properties of angles for a quadrilateral inscribed in a circle.
• G-GPE.1: Students are asked to derive equations using the distance formula rather than the Pythagorean theorem.

The materials, when used as designed, partially meet the expectation for allowing students to fully learn each non-plus standard. In general, the series addressed many of the standards in a way that would allow students to learn the standards fully. However, there are cases where the standards are not fully addressed or where the instructional time devoted to the standard was insufficient. The following are examples where the materials partially meet the expectation for allowing students to fully learn a standard.

• N-Q.2: Students are given opportunities to work with appropriate quantities when creating models for problems. However, many of these quantities are prescribed for students rather than allowing students to define their own quantities. This prescriptive definition by the materials does not allow students to develop their own understanding of how the quantities relate to the problem.
• A-SSE.1b: Students are given minimal opportunities with this standard. An example is in Algebra 2 on page 228 where students are asked to use the discriminant to determine the nature of the solutions. Students are not asked to interpret other expressions throughout the series.
• A-APR.4: The standard requires that students prove polynomial identities. There is one instance of this proof in Algebra 2 on page 251. This example proved the exact identity in the example in the standards. There are no other examples for proving identities. Students are also not given the opportunity to produce these proofs on their own.
• A-REI.10: The one reference found for this standard is the Math Tip on page 92. There is no additional work to help students understand that the graph produced contains all possible solutions to the given equation.
• F-IF.2: While students are given opportunities to evaluate functions, there are very few opportunities for students to interpret the given function in terms of the context of the given problem. In the instances where students were asked to interpret an equation in terms of a given context, function notation was not used, which is part of the standard.
• F-IF.5: Students are not asked to determine the relationships between the domain and a graph.
• F-LE.1a: There is one instance where students are exploring that linear functions grow by equal differences over equal intervals in Algebra 1, Lesson 9-3.
• F-TF.8: There is a proof of the Pythagorean identity as part of the standard. In the materials, this proof is provided for the students. Students are not given the opportunity to construct the proof of the Pythagorean identity.
• S-CP.5: Students are given the opportunity to calculate the conditional probability; however, they are not given sufficient opportunities to interpret their answers in terms of the context of the model.

There are also two examples of the materials including content that is distracting because the content is not part of the CCSSM for high school.

• In Geometry, lesson 12-1 on page 167, the learning targets are "Write a simple flowchart proof as a two-column proof. Write a flowchart proof." While these are very explicit indications of the content in this lesson, there is no reference to specific types of proofs in the CCSSM.
• In Algebra 2, lesson 19-3 on page 303, the learning targets are "Identify the index, lower and upper limits, and general term in sigma notation. Express the sum of a series using sigma notation. Find the sum of a series written in sigma notation." The language of the learning targets and the content of the lesson are not a part of the CCSSM.

The following are some examples of where the materials meet the expectation for allowing students to fully learn the standard:

• G-CO.9: Starting with Lesson 6-1 in the Geometry materials, students are given multiple opportunities to use different properties and prove simple theorems about lines and angles. In Lesson 6-2, students are introduced to the Vertical Angles Theorem and use the theorem in other proofs about lines and angles. In Lesson 7-1, the materials address different angle pairs formed when a transversal intersects parallel lines and the relationships between the pairs of angles. In the remainder of the Geometry materials, there are various places where students use relationships already proven to prove new theorems about lines and angles.
• N-Q.3: This standard is completely addressed in all courses. In Algebra 1, there is an explanation on page 489, problem 3d, in both the student and teacher editions discussing how to choose the appropriate level of accuracy. From that point on, students are expected to choose an appropriate level of accuracy in remaining lessons and courses.
• F-IF.8 is only identified in the online version of the materials. The standard was fully addressed in the materials in the online version where identified.

The instructional materials partially meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Although students are able to experience the majority of the standards they would need to master in order to be college- and career-ready, there were several instances where students did not get to engage with content in a way that is appropriate for high school students.

Examples of where this series partially meets the expectation include:

• Standards that require students to prove concepts or provide explanations were not fully developed and did not allow students to engage with the content in order to master the standards. An example of this is G-CO.9 where mostly teacher-given proofs were used (very few opportunities for students to generate their own proofs). G-SRT.7, problem 8, on page 310 of the Geometry textbook is one item that addresses this standard, and while the answers to problems on pages 312 and 313 address this standard as well, the explanation required from students would not fully address the relationship between the sine and cosine of complementary angles.
• While the context provided for application problems is appropriate for high school, the contexts do not motivate the mathematics. For example, many of the Geometry contexts are superficially connected to the topic as the lessons could be completed without any knowledge of the context.
• Most problems provide students with scaffolded steps and lead the students to the answers. For example, in the Algebra 1 textbook, lessons 7-1 and 7-2 provide students with tables, either completely or partially populated, and graphs that are completed or, at least, have scales marked and axes pre-labeled.
• Problems presented in each section have routine answers and do not challenge students to engage fully in the mathematics required to be college- and career-ready. For example, in the Algebra 1 textbook, lesson 7-3, The Radioactive Decay Experiment, focuses on the concept of half-life for radioactive substances, but the problems in the lesson consistently use initial amounts that are even integers, which makes the computations and resulting answers much simpler than if the initial amounts were odd integers, fractions, or decimals.

When information is provided for differentiated instruction, the content does not replace what students are expected to learn in order to be college and career ready.

• The "Getting Ready Practice" available for most units and topics is often below grade level, but it is also clearly labeled as "additional lessons and practice problems for the prerequisite skills." For example, there are "Getting Ready Practice" lessons on the distributive property (Grade 6) and operations with decimals (Grade 5), along with operations on polynomials (grade-level for Algebra 1) and graphing linear functions (Grade 8, deeper in Algebra 1). Many of the Geometry "Getting Ready Practice" topics are from the Grade 7 and 8 Geometry standards. Many of the Algebra 2 textbook "Getting Ready Practice" topics are from Algebra 1 content, but several are grade-level, such as determining asymptotic restrictions and finding inverses of functions.
• Information presented in the sections labeled "Differentiating Instruction" or "Adapt" is not intended to replace the course-level work that students should be doing to master the standards. "Differentiating Instruction" contains directions to extend grade-level learning, and "Adapt" guides the teachers to check that students understand certain concepts and offers suggestions as to how to support students who need extra practice or what to do if re-teaching is required.

The instructional materials reviewed partially meet the expectations that the materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and required by the Standards.

The organization of the course materials categorize units of study by related topics, and many of the activities cite multiple standards in the overview. Connections between clusters and domains are not always made for the teacher or student, and missing connections decrease the coherence of the materials across courses. The following are examples of missed opportunities for coherent connections throughout the series.

• Although there are locations in the Algebra 1 materials where Statistics and Probability standards could be explicitly associated with the Algebra and/or Functions standards, the connections were not made. For example, a connection between standards in the Functions and Statistics and Probability categories could occur in Algebra 1, lesson 13, "Equations from Data," but it does not.
• There are missed opportunities to connect the Statistics and Probability and Number and Quantity categories. The relationship between N-Q.1, N-Q.2, and the Statistics and Probability standards could have been made clearly in many places in Algebra 1, Unit 6. Students are working with data, yet no mention is made to whether or not the measures of center are reliable for different distribution shapes or to level of accuracy that can be expected from a line of fit for less-than-nearly-perfect correlations.
• There are few connections between Geometry and other conceptual categories. Examples of missing connections are:
  • Proofs about various aspects of mid-segments in triangles (G-CO.10) are present in Geometry, lesson 15-1, but there are no Algebra or Functions standards listed in the lesson, such A-SSE.3 as F-IF.6.
  • Geometry activity 26 is entitled "Coordinate Proofs" and contains algebraic proofs for midpoint, slope, and concurrency (G-GPE.4,5); however, there are no Algebra or Number and Quantity standards listed in the activity, such as A-SSE.1 or N-RN.2.
  • Geometry, activity 27 uses a coordinate plane to develop the equation of a circle (G-GPE.1), which ties together the Geometry and Algebra categories through the process of completing the square, but there are no specific connections made concerning these concepts, especially A-REI.4.
  • Geometry activity 28 and Algebra 2 activity 10 (both on using focus and directrix to write the equation of a parabola) are linked, but the materials do not explicitly connect the two activities.

Some examples of how the content is coherent and provides opportunity for students to make meaningful connections are as follows:

• In the Geometry textbook, Unit 3 is titled "Similarity and Trigonometry." Having these topics in the same chapter provides evidence that the content of the materials has been structured in terms of the connections and coherence inherent to the standards. After students learn about similarity, they engage in content specific to similarity in right triangles, which then leads to defining trigonometric ratios as a result of "understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle."
• In Algebra 2, connections are made in the "Getting Ready" part of many sections. Unit 6 (page 476) recalls work done in Geometry (G-SRT), Algebra (A-SSE and A-CED), and Functions (F-BF), and page 477 states in the teacher materials that "students will use what they have learned in previous courses about circles, circumference, central angles, and arcs."
• In the Algebra 1 textbook, quadratic functions are introduced through context, data, and modeling with mathematics (Lesson 29-1). Then students move into analyzing and looking at properties of quadratic functions (Lesson 29-2). In activity 30, they look at transformations of quadratic functions in the coordinate plane. Then, in activity 31, students factor quadratic expressions to find the x-intercepts of the function defined by the expression. In activity 32, students complete the square to find the vertex of a quadratic function. The portions of the materials involving quadratic functions attend to the coherence in the standards, and students have been given opportunities to see structure in expressions and think about different forms of equivalent expressions.

The instructional materials reviewed for the series partially meet the expectation that the materials explicitly identify and build on knowledge from Grades 6-8 to the high school standards. The materials miss opportunities to identify knowledge from previous grades and move the students’ learning forward.

Below are examples of where the materials do not identify knowledge from Grades 6-8 and do not use the prior knowledge to move learning forward:

• In Algebra 1, activity 9, the materials do not explicitly identify that students are building on their work with slope from Grade 8. The slope and rate of change portions of 8.EE.B and 8.F are not listed in the prerequisite skills for the unit. The activity does have students build on their knowledge of slope from Grade 8 to engage in F-IF.6 and F-LE.1.
• In Algebra 1, activities 14 and 15, the materials do not identify any standards from 8.F where students defined, compared, evaluated, and used linear functions to model relationships between quantities. This domain from 8^th grade forms the basis for the extension of linear concepts into piecewise-defined linear functions that occurs in activity 14 and comparing equations that occurs in activity 15.
• In Algebra 1, activity 17, the materials do not identify any standards from 8.EE.C where students analyzed and solved pairs of simultaneous linear equations. In addition, lessons 4 and 5 in activity 17 are the only lessons that move student learning beyond what is addressed in 8.EE.C as these two lessons have students examine systems of linear equations without a unique solution and classify systems of equations, respectively.
• In Geometry, activity 9, the materials do not identify any standards from 8.G.A or 6.NS.C where students understand congruence and similarity through transformations and recognize reflections across the axes, respectively. These clusters form the basis for the learning around transformations that occurs in activity 9.
• In Geometry, activity 20, the materials do not explicitly identify that students are working with the Pythagorean Theorem from Grade 8. The work from Grades 6-8 is treated as a separate topic to review as opposed to being a foundation for new learning.
• In Algebra 2, activity 25, the materials do not identify any standards from 8.EE.A where students work with radicals and integer exponents. This cluster forms the basis for working with square root and cube root functions that occurs in the four lessons of activity 25.

Each unit begins with a “Getting Ready” section that reviews prerequisite skills needed to engage in the mathematics of the upcoming section. The skills are aligned to previous grade-level CCSSM standards. Additional “Getting Ready” practice pages are available in the digital teacher resources. Although these skills are identified in the “Getting Ready” sections, connections are not made between the problem sets and the activities or lessons.