The Instructional materials reviewed for Pearson Integrated High School Mathematics Program partially meet the expectation that the materials attend to the full intent of the mathematical content contained in the high school standards for all students. For this indicator, the resource book titled "Implementing the Common Core Standards with Persons Integrated" was used, and it includes a table that shows where in the series standards are found. Additionally, the teacher edition lists the standards addressed in each section. The identified sections were examined for evidence of each standard's existence and the extent to which the full depth was met. At times, what is stated in the resource book does not match the standards stated for each section in the teacher edition. Overall, some standards where completely omitted from the materials, and some aspects of the non-plus standards were not completely addressed by the instructional materials of the series.

There are standards in the materials that are addressed thoroughly. Some examples of those include:

• Mathematics II book provides several lessons on circles that focus on G-C.2. All examples listed in the standard are addressed in the book.
• Mathematics II, chapter 9 provides students several problems involving real-world representations that have the exact shape of the figure as stated in G-MG.1. (For example, lesson 9.1 uses a paint roller for a cylinder and a pencil for a hexagonal prism. Lesson 9.2 uses a chemistry funnel for a cone).
• F-IF.1-3 are addressed in Mathematics I, chapter 2. The teacher edition provides additional explanation of the recursive formula while the student material provides opportunities for reinforcement of these standards.
• All A-CED standards are continually addressed throughout the series, requiring students to create equations across other domains.

There are standards that are partially addressed but omit required aspects listed in the CCSSM. Some examples of those include:

• Mathematics I, Lesson 8.2 and 8.3 address G-CO.4 by giving students the opportunity to begin developing their definitions of reflection and rotation, but not translations.
• Standard G-CO.12 calls for students to "Make formal geometric constructions with a variety of tools and methods" (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Opportunities in the series for students to use geometric software were very limited.
• Mathematics III contains problems where students use graphing calculators and may have to adjust the graphing window in order to find or interpret the maximum, minimum, and/or zeroes of functions; however, there wasn't evidence that students are required to use units as a way to understand problems and to guide the solution of multi-step problems as stated in N-Q.1.
• Mathematics III, Lessons 1.4 addresses S-ID.4. Only two problems require students to use graphing calculators to estimate areas under the normal curve, and there are not opportunities provided for students to use spreadsheets.
• Mathematics I, In Lesson 6.1, students are required to "interpret differences in shape, center, and spread in the context of the data sets" as stated in S-ID.3; however, the instructional materials are lacking opportunities for students to account for possible effects of extreme data points.
• Mathematics III, Lesson 1.1 and 1.2 provide students with pieces of data based on multiple scenario; however, opportunities for students to evaluate a report based on data as S-IC.6 indicates were not located.
• The materials lack opportunities for students to experience the full intent of A-SSE.1. The examples that were found were frequently void of context. The exercises that are written in context do not require students to interpret the meaning of an expression or parts of an expression but rather to rewrite or to solve.
• Though students must rewrite rational expressions in different forms in lessons 4.5 and 5.1 of Mathematics III, A-APR.6 is not fully addressed. Students use long division to divide polynomials, not written in rational form as the standard states, in lesson 4.5. Lesson 5.1 has students using factoring to simplify rational expressions.
• Students are exposed to the idea of the rates of change for linear and exponential functions in Mathematics I, Lesson 5.3; however, they are not asked to "prove" how linear and exponential functions grow over equal intervals as indicated in F-LE.1a.
• In Mathematics III, page 653 of student edition, the Pythagorean identity mentioned in F-TF.8, is given to students; they do not prove it as required by the standard. Students are then asked in problems 44 - 49 to use the given identity to verify each of the other Pythagorean identities listed in F-TF.8.
• Solving systems of equations, A-REI.6, is addressed in Mathematics I, Lessons 4.1-4.5. There are examples of students finding exact solutions to a system of equations algebraically and through the use of graphs, tables, and technology. However, no references to solving systems "approximately" as stated in the standard were found.
• A.REI.11 expects students to "explain why the x-coordinates...are the solutions." This fact is used in the series (Mathematics I, 2.4 Lesson Lab, Mathematics III, Lesson 4.4, Mathematics III, Lesson 5.7), but students are not expected to explain "why."
• Mathematics I, Lesson 5.2 (F-IF.7e) asks students to graph exponential functions, but students are not explicitly expected to show intercepts and/or end behavior. Mathematics III, Lesson 7.1 is also listed as addressing this standard but also does not explicitly address these facts.
• Arithmetic and geometric sequences are addressed in Mathematics I, Lesson 5.6, Mathematics II, Lesson 15.2 and 15.3 (which is identical to Mathematics III, Lessons 9.2 and 9.3). In these sections, students write both explicit and recursive formulas to model situations; however, reviewers were unable to find evidence of translating between the two forms as stated in F-BF.2.
• G-SRT.4 requires students to "prove theorems about triangles" including "a line parallel to one side of a triangle divides the other two proportionally and its converse" which the materials prove for the student in Mathematics II, Lesson 6.5. The materials then allow students to prove the converse in problem 36 of Lesson 6.5. The standard also specifically calls out proving the Pythagorean theorem using triangle similarity, yet there is no evidence of this in the materials.

For the following standards, certain sections were identified as addressing a specific standard by the publisher, however, the standard was not present.

• G-CO.4
• G-CO.10
• G-SRT.1
• S-IC.2
• A-SSE.1b
• G-GPE.4 is a non-plus standard; however the publisher indicates in the CCSS resource book that this standard is not included in this series and is "studied in a 4th year course." The Mathematics III, Lesson 11.4 teacher edition does reference alignment to G-GPE.4; however, this section does not require any proof as is stated in the standard.

The Instructional materials reviewed for Pearson Integrated High School Mathematics Program partially meet the expectation that the materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, post-secondary programs, and careers.

For this indicator, reviewers looked at the frequency of exposure to the WAPs throughout the series in order to determine if the majority of time was spent on these standards. Throughout the materials, multiple chapters are duplicated from one book to the next. As a result, any WAPs addressed in those duplicated chapters were only considered once.

The following WAPs were thoroughly incorporated into the materials:

• Each domain in the Algebra category is thoroughly incorporated throughout all materials. Creating equations standards are consistently embedded throughout the series, offering students multiple opportunities to create equations to describe relationships using a variety of function families. In addition, several of the Pulling It All Together problems embed various Algebra standards.
• S-ID.2 is present in multiple sections of Mathematics I, chapter 6

The following WAPs are found to be lacking throughout the materials:

• Functions: Most of the function standards have only a limited number of problems throughout all of the materials. For example, F-IF.1 and F-IF.2 are present in one section, F-IF.3 is present in two sections, F-IF.4 and F-IF.5 have one problem that meet the standard, and F-IF.9 is present in two problems.
• Geometry: Most of the Geometry standards have a limited number of problems in the materials. For example, G-SRT.B is addressed partially in two sections throughout the materials (Mathematics II, Lesson 6.5 and 7.1), and G-SRT.C are minimally present in Mathematics II, Lesson 7.3 and 7.4.
• Number and quantity: Complex Number System standards (N-CN) are present in one section throughout the materials. Real Number System standards (N-RN) are partially addressed in Mathematics II, Lessons 10.1-3.
• Statistics and Probability: Students are provided limited opportunities with S-ID.7 and S-IC.1. For example, S-ID.7 is present in Mathematics I, Lesson 6.7 and only three questions in Lesson 3.1. S-IC.1 is present in Mathematics III, Lesson 1.3.

The middle school WAP standards throughout the materials are not treated as a review but fully taught as if the students have never experienced them before. At times, the materials list sections as review, and other times they labeled review material as high school standards when it is not.

• Mathematics I features several sections that review middle grades content, although they identify with high school standards. (Sections 1.1, 1.2, 1.3, 1.5, 1.6, 2.3, 2.4, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 5.1, 7.1, 7.6, 9.2, and 9.3). Sections 7.1, 7.6 and 9.2 state that they are preparing students for high school standards. A review of previous standards may be necessary, but the review should be labeled as review. Having 19 lessons devoted to review in Mathematics I is a distraction from the standards that need to be addressed. The focus should be on the standards for high school. The distributive property is addressed in 1.1. Students have been working with the distributive property for several years. And 1.5 and 1.6 (ratios, rates, conversions and proportions) also address standards students would have spent an extensive amount of time on in previous grades, so these topics should be treated as review and not as new content for the students.
• Some sections do not delve deeply beyond the middle grades expectations. For example, Grade 8 students are expected to be able to solve linear systems of equations algebraically and through graphing. In Mathematics I, chapter 4, the information is presented as though this is new content, spending three out of six sections teaching three methods for solving systems. In addition, the problems only require integer solutions—students are not expected to deal with rational solutions which would be appropriate for the high school level.

The Instructional materials reviewed for Pearson Integrated High School Mathematics Program partially meet the expectations that the materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics. Some standards were incorporated into the materials in a way that provides students the opportunity to engage in the full intent of the standard. However, for some standards there were not enough exercises for the students to fully learn the standard. Additionally, in most cases where the standards expect students to prove or develop a concept the materials simply provided students the information. Also seen as distracting are the sixteen repeated chapters and multiple repeated labs.

• In the Mathematics II book, 7 of the 15 chapters are duplicated word-for-word what was in the Mathematics I book, therefore only 8 chapters in the Mathematics II book consist of new content. Listed in the table below are the duplicated chapters.

The following standards were included in the materials, yet were not presented in a way that would allow students to fully learn that standard.

• Even though chapter 3 in Mathematics II is titled "Congruent Triangles," the section where students are proving triangles congruent through the use of transformations, as called for in cluster G-CO.B, is section 3.8. The rest of the chapter offers proofs that are not required by the CCSSM.
• Students are not required to prove for themselves the theorems outlined in G-CO.9-11. The materials provide the proofs and then ask the students to use the proven theorems. The only theorem that students are asked to prove is that alternate exterior angles are congruent; however, this theorem is not specifically included in the standard.
• Mathematics II, Lesson 6.6 and the activity lab address dilations, yet instead of focusing on experimenting to find the properties of dilation, as stated in the standard G-SRT.1, the properties are stated for them in section 6.6.
• G-C.5 requires students to "derive using similarity" arc lengths of circles; this experience is completed for the students in Mathematics II, Lesson 8.1. Lesson 8.2 then defines radian for the students.
• G-GPE.2 requires students to "derive the equation of a parabola given a focus and directrix;" this experience is completed for students in Mathematics II, Lesson 12.11.
• Mathematics II, Activity Lab for 9.1 provides students the opportunity to "give an informal argument for the formulas for the circumference of a circle and the area of a circle" as stated in G-GMD.1. Students have limited opportunities to develop informal arguments for formulas. Mathematics II, Lesson 9.3 and 9.4 provides students with the formulas for the the volume of a cylinder, pyramid, and cone.
• S-ID.8 requires students to "compute (using technology) and interpret the correlation coefficient"; the materials demonstrate how to calculate the correlation coefficient of a linear fit using a graphing calculator in Mathematics I, Lesson 6.4, yet the only opportunity for students to interpret the correlation coefficient is problem 19, part c in section 6.4.
• Mathematics I, 5.4 lesson lab and Mathematics III, Lesson 7.2 provide students minimal opportunities to use exponent properties to transform expressions for exponential functions as required by A-SSE.3c.
• A-APR.4 requires students to "prove polynomial identities and use them to describe numerical relationships." Mathematics III, 4.6 Lesson Lab provides students with the polynomial identities. Students are then expected to use the given identities to prove numerical relationships.
• Evidence of F.LE.1b was found in one problem throughout the series, Mathematics I, 3.1 problem 9 in practice A.

The following standards provide students thorough exposure through multiple experiences to fully learn each standard.

• The Mathematics II book does a good job covering G-SRT.5. Seventeen different sections (3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 4-1, 4-2, 4-4, 5-1, 5-2, 5-4, 5-5, 5-6, 6-2, 6-3 and 6-4) in the book work together to address this standard.
• Mathematics III contains 13 chapters. Nine of the labs require students to use graphing calculators and one lab requires a spreadsheet as tools to further address F-IF.7, F-IF.7b, F-IF.7d, F-IF.8, F-BF.3, A-CED.1, A-REI.11 and S-ID.6b. Some of these Labs (4-1 technology lab and 5-7 technology lab) provide mathematical problems that have multiple solution paths and ask students to complete problems graphically and algebraically to address F-BF.3 and A-CED.1.
• Students have ample opportunities throughout this series to complete standards A-CED.1 and A-CED.2. Throughout the materials students are expected to write equations and solve them. They write linear equations, proportions, absolute value, exponential, quadratic equations, and inverse variations. Most sections give students several opportunities to practice writing and solving equations and inequalities in one and two variables.

The materials offer additional resources to help all students fully learn each standard.

• The series provides guidance to teachers at the beginning and end of each lesson on how to support ELLs and ideas for differentiated remediation, thus giving opportunities for all students to fully learn presented standards. Each "Preparing to Teach" section contains an "ELL Support" section that calls out things like the possible use of manipulatives, connecting to prior knowledge, focusing on communication, using graphic organizers, etc. Even though these are suggestions in reaching ELL, they are strategies to help reach all learners.
• The end of each lesson quiz has guidance for teachers to place students at intervention, on level, or extension level. Teachers have online access to reteaching and additional vocabulary support worksheets for students needing intervention, extra practice worksheets for students on level, and activities, games and puzzles as well as enrichment worksheets for extension opportunities. Enrichment worksheets provide higher depth of knowledge questions on grade level, while reteaching worksheets provide low depth of knowledge questions which are at times below grade level. These items can aid in ensuring all students fully learn the intended standards.
• Students can also access virtual nerd tutorials and homework video tutors (in English and Spanish) online as needed. Each student edition has a "Visual Glossary" of all terms in English and Spanish, complete with definition and visual example and page number of where the term appears thus possibly helping many students better learn a standard.

The Instructional materials reviewed for Pearson Integrated High School Mathematics Program partially meet the expectation that all students engage deeply with the non-plus standards. Overall, the contexts of the scenarios are appropriate for high school students. There are resources available for special populations, but at times they distract from the full intent of the non-plus standards. Problems too frequently involve integer solutions where real-world problems tend to involve more complicated solutions.

• To help students engage with the non-plus standards, the materials include a lesson check and practice at the end of each section. Additionally, the materials provide online resources for remediation and extension, including online problems (pearsonsuccessnet.com), reteaching (online teacher resources), practice (online teacher resources), and Challenge Problems. These resources better allow students a chance to practice with a variety of problems related to the lesson. The problems presented are not repetitive and often include real-world word problems.
• The problems provided for students throughout the series often have answers that are whole numbers. The publisher does provide a few problems throughout the series that have decimal or fraction answers, but these problems usually are limited to one or two decimal places. Real life problems often do not result in whole number answers and many times have very long decimal answers. The linear equations that are graphed throughout the book often have whole number x and y intercepts. Units are often consistent as well, not requiring students to convert units prior to solving. Functions intersect at integer values.
• The contexts of many real world problems are appropriate for high school students and often involve topics that students would find interesting such as architecture, agriculture, sports, cell phones or careers.
• The time spent on the domains within the number and quantity category is not balanced. There are few opportunities to work in the real number system domain (four lessons and one activity lab in Mathematics II) and the complex number system domain (Mathematics II one lesson) but many opportunities to work in the quantities domain (21 lessons and one activity lab throughout the series).
• The Statistics and Probability conceptual category is not balanced when compared to the Functions, Algebra, and Geometry conceptual categories. There are far fewer opportunities to work with Statistics and Probability standards throughout the materials.