The instructional materials reviewed partially meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. While some components of the modeling process are frequently required of students, students are not required to go through all of the steps as outlined by the CCSSM.

Aspects of the modeling process that are frequently addressed throughout the series expect students to formulate, compute, interpret and validate in problems.

• In many For You to Do problems and chapter projects, students are encouraged to develop their own solution strategy - formulate and compute. In the Algebra 2 Chapter 3 Project, students are asked to use their knowledge of factoring to factor polynomials of the form x^n-1, identify patterns, and formulate a conjecture relating the number of factors of x^n-1 to the number of factors of n.
• In many lesson discussions, students are interpreting and validating findings. Very often students have to critique the process that the fictional students in the materials use to solve problems. In Algebra 1, Lesson 4.02, students have to determine who correctly found the slope in a the problem given.

Although the components of the modeling cycle are included, the entirety of the modeling cycle was not located throughout any of the materials.

The Instructional materials reviewed partially meet the expectation for allowing 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 (WAPs). Overall, there are parts of the materials that address topics which are distracting from spending the majority of the instructional time on the WAPs.

Some examples of topics that are distractions from the WAPs are as follows:

• In Algebra 1, Chapter 1 allots 16 instructional days (according to the publisher's pacing chart) to arithmetic rules for integers, decimals and fractions. This material does not align to the high school CCSSM, so it is distracting from the WAPs.
• In Algebra 1, Chapter 2 allots 17 instructional days (according to the publisher's pacing chart) on simplifying expressions and solving equations. The majority of the questions in this chapter utilize linear expressions and equations which more closely align to standards from grades 6-8.
• In Geometry, lessons 3.01-3.08 address cutting/rearranging figures to compose new figures and use this as a lead-in to area. Thirteen instructional days (according to the publisher's pacing chart) are dedicated to these lessons, but these lessons align more closely with standards from grades 6-8.
• In Algebra 2, lesson 4.03 solves systems of equations using matrices, and lessons 4.04-4.13 address algebra with matrices and applications of matrices. The materials allot 11 instructional days (according to the publisher's pacing chart) to these lessons which align to plus standards.
• In Algebra 2, lessons 6.05-6.10 address affine transformations which are beyond what is required by the standards. The materials allot six instructional days (according to the publisher's pacing chart) to these lessons, and they are distracting from the WAPs as the transformations explored are beyond the requirements of the CCSSM.

In addition to including topics that are distracting from the WAPs, the instructional materials, when used as designed, include insufficient opportunities for students to engage with the WAPs as the number of instructional days allocated to each course varies greatly.

• In Algebra 1, the instructional materials reviewed are designed to be completed in 119 days.
• In Geometry, the instructional materials reviewed are designed to be completed in 157 days.
• In Algebra 2, the instructional materials reviewed are designed to be completed in 114 days.

The instructional materials reviewed partially meet the expectation for, when used as designed, allowing students to learn each standard. Overall, the instructional materials provide limited opportunities to practice several standards.

In the instructional materials, examples of standards with limited opportunities for practice include, but are not limited to, the following:

• F-IF.3: The lessons this standard is aligned to by the publisher address recursive functions, but sequences are not the emphasis nor were they defined. The fact that the domain is the subset of the integers was not made explicit, either. It is not aligned to Algebra 1, lessons 5.07 and 5.08 as denoted in the teacher edition. It is aligned to lesson 5.09.
• F-IF.4: Instructional materials provide several opportunities to graph different types of functions; however, students are not always asked to identify key features. In Algebra 1, lessons 8.06-8.08, students are asked to determine where a function is increasing/decreasing, find maximums and minimums, find the line of symmetry, and determine zeros of a quadratic function. In Algebra 2, lessons 5.07 and 5.14, students are asked to determine whether a logarithmic or exponential graph is increasing or decreasing as well as determine the domain of these two types of functions when graphed. No other functions are interpreted for increasing/decreasing intervals, end behavior, maximums/minimums, symmetries, or end behavior.
• F-IF.5: Algebra 2, lesson 2.02 has students graph a function, find the domain, and reverse the process by finding the domain of a function and then graphing. Algebra 1, lesson 8.06 is misaligned (no examples in which students relate domain to a graph). Throughout the series, no examples were identified in which students need to interpret domain of a function provided within a context.
• F-IF.7b: Although instructional materials show students how to graph square root functions and absolute value functions, there is limited practice provided and may not be sufficient for every student to master the content of the standard.
• F-BF.1b: Although Algebra 2 lesson 2.08 has students combine functions using arithmetic operations, this section provides limited practice that may not be sufficient for every student to master the content of the standard.
• F-BF.3: The publisher aligns Algebra 1 lessons 3.16 and 3.17 to this standard. In these two sections, selected problems in the "Maintain Your Skills" portion of the materials (lesson 3.16, problems 17 and 18; lesson 3.17, problem 16) have students graph functions that have been translated or stretched from a parent function. However, there is no instruction on generalizing these effects until lesson 3.18. Students are expected to use a graphing calculator to complete these problems and don't rely on their knowledge of the "rule" for translating and/or stretching graphs. These skills are later addressed in Algebra 2 lessons 6.01, 6.03 and 6.04.
• F-LE.5 Interpreting parameters in an exponential function in terms of a context is mainly limited to compound interest.
• A-APR.4: There are limited opportunities to prove polynomial identities (correlation guide lists Algebra 1 lesson 7.01, problem 14 and Algebra 2 lessons 2.11, 2.13, 2.14, but also found in Algebra 1 lesson 7.02 pages 614-615).
• N-Q.1: There is evidence of using units appropriately in all three textbooks; however, using units is not emphasized as a guide to solving multi-step problems throughout lessons.
• N-Q.2: Defining appropriate quantities for descriptive modeling is limited to rates of change (Algebra 1 lesson 4.03). [Algebra 2 lessons 1.07 and 1.11 are specified by the publisher correlation to be aligned to this standards but evidence of this standard was not found in the lesson.]
• N-CN.7: Limited opportunities are provided for students to solve quadratic equations with complex solutions. Algebra 2 lesson 3.03 first introduces solving quadratic equations that have complex solutions. Subsequent lessons in Chapter 3 have students practice these skills in the On Your Own exercises and Maintain Your Skills exercises. Algebra 2 lesson 3.04, problem 15 and 3.07, problems 10 and 11.

A lack of consistency with how lessons are labeled in the teacher materials could also impede students from fully learning each standard because lessons that allow for the full depth of the standard to be realized are identified as optional. This type of inconsistency occurred several times throughout the courses. For example, in Algebra 1, Chapter 4 Investigation 4D (lessons 13-15) is noted as optional in the materials with the lessons (page 394). However, the lessons are not noted as optional in the pacing guide at the beginning of the chapter or book, and the standards for these lessons in the alignment guide are identified as met (not optional).

The instructional materials reviewed partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to high school. In general, the Algebra 1 materials tend to spend excessive time reviewing the grade 6-8 standards while Algebra 2 tends to do the opposite, including many of the plus standards and extending the instruction beyond what is expected for the high school mathematics standards.

• There are a significant number of lessons and problems aligned to middle school content and/or considered prerequisite skills. In Algebra 1, lesson 1.08, for example, students are asked to convert decimals to fractions. They are also asked to plot numbers on a number line. Neither of these tasks align to a high school standard. Most lessons that align to middle school content are included in the Algebra 1 course; the lessons in the Geometry and Algebra 2 courses do not have a significant amount of content that aligns to middle school standards.
• The end-of-chapter project in Algebra 2, Chapter 7 goes beyond the scope of the high school mathematics standards and contains notation and formulas that extend past the appropriate level of mathematics for a high school course. The project contains tasks that lead to a proof of "for any set of data, the line of best fit contains the balance point." The line of best fit is appropriate to high school. Then the students are asked to find the centroid and the error for each point. From there, the materials go on to find the sum of squares which, with the notation and equations, addresses plus-standards and beyond.
• The units and lessons aligned to the non-plus high school standards generally feature a range of activities that address procedural knowledge, conceptual understanding, and problem solving. For example, Algebra 1 Unit 2, titled “Expressions and Equations,” has lessons that address A-CED.1 and A-REI.1, two standards that deal with solving equations. Lesson 2.09 includes some number puzzles that introduce the topic. Lesson 2.10 gives models intended to help conceptually understand the logic of equation solving, while lessons 2.11 and 2.12 focus more on the procedures involved in solving equations and lessons 2.15 an 2.16 address solving word problems by solving equations that model the word problems. The context, numbers used, and habits of mind addressed engage students in mathematics at a level of sophistication appropriate to high school.
• The diversity of numbers, representations, and equations in the materials is appropriate for high school. Expressions and equations used throughout the series incorporate integers, decimals and fractions.

The instructional materials reviewed partially meet the expectations for fostering coherence through meaningful mathematical connections in a single course and throughout the series, where appropriate and where required by the Standards.

In some cases, the lessons do provide mathematical coherence between and within courses. Some examples include:

• Algebra 2, lesson 4.01, begins with a link back to Algebra 1. The lesson addresses solving systems of equations, and then the chapter moves into an emphasis on using matrices to solve similar problems.
• Algebra 2, lesson 5.12, connections are made between the properties of logarithms and the connection to the properties of exponents that were addressed earlier in the chapter showing that connections are made within the course.
• Algebra 1, Chapter 8 has students solve quadratic equations, and Algebra 2 extends to including solving quadratic equations with complex solutions.
• Another example that shows coherence but lacks explicit connections is in an introduction to exponential expressions and functions in Algebra 1 and 2. Algebra 1, Chapter 6 provides the framework for a more deeper understanding of exponential functions in Algebra 2, Chapter 5.

However, connections to prior course and series learning is not always explicit for teachers and students. For example, lessons on scatterplots and positive versus negative associations of data are introduced before lessons on slope and graphing lines in Algebra 1. This builds the foundation for learning about best fit lines in lessons 1.06-1.09 in Algebra 2; however, these connections are not explicit for teachers or students.

Some examples that demonstrate that the lessons are not always coherent include:

• Geometry lessons 2.15 - 2.19 addressing quadrilateral properties do not continue the coherence of the lessons in the beginning part of the chapter on congruence and proof.
• Conceptual understanding of area builds in the Geometry materials as students learn about area formulas in lessons 3.06-3.08, then coordinate geometry in lessons 7.06-7.10, and applying this knowledge in optimization examples related to area in lessons 8.04-8.06. Although the concept of area is part of each of these lessons, the lessons do not build on one another nor provide teachers or students prompts for recalling information about area from previous lessons.
• Not all Statistics and Probability topics fit coherently throughout the courses. Interpret Linear Models (S-ID.7-9) fits naturally into the Graphs and Lines units, but Summarize, represent, and interpret data (S-ID.1-6), which includes mean, median, and two-way frequency tables, is not as natural a fit in those units.

The instructional materials reviewed partially meet the expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards.

For example, Algebra 1, Chapter 1: Arithmetic to Algebra addresses basic arithmetic of integers, fractions, and decimals. The pacing guide in the teacher edition of the materials indicates that these lessons build upon grades 6-8 standards in order to prepare for a high school content standard. For example, Lesson 1.05: The Basic Rules of Arithmetic "builds on 6.EE.3, 7.NS.1, and 7.NS.2 to prepare for A-SSE.2 and A-APR.1." Furthermore, the instructional materials sometimes, but not always, indicate when lessons review grades 6-8 content. For example, Algebra 1 lessons 4.01 and 4.02 review 8.EE.6. In Algebra 1, the pacing guide aligns the entire first chapter as "builds on" standards for grades 6, 7 and 8. There is not notation in the chapter or individual lessons that reiterates that the content is review or preparation for later lessons.

Not all connections from content taught in grades 6-8 and high school are clearly and explicitly articulated. For example, Investigation 3C in Geometry has students build upon their knowledge of the Pythagorean theorem developed in Grade 8 by investigating several different proofs of the theorem. However, no connections are explicitly made between the Grade 8 cluster "Understand and apply the Pythagorean Theorem" and the high school domain G-SRT: Similarity, Right Triangles, and Trigonometry.