Alignment: Overall Summary

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not meet the expectations for alignment to the CCSSM. In Gateway 1, the materials do not meet the expectations for focus and coherence. The materials do not meet the expectations for focus and coherence as they do not meet the expectations in the following areas: attending to the full intent of the modeling process when applied to the modeling standards, 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. Since the materials did not meet the expectations for focus and coherence, evidence for rigor and the mathematical practices in Gateway 2 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
6
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
21
30
36
N/A
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional 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" (p. 57 of CCSSM).
6/18
+
-
Criterion Rating Details

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not meet the expectation for Focus and Coherence within the CCSSM. For focus, not all of the high school, non-plus standards are taught to the depth expected in order to give students the opportunity to fully learn each standard. Context of problems are appropriate for high school students; however, the numbers used to model situations are simplistic. The full intent of the modeling process is minimally applied to the modeling standards. The materials contain multiple repeated chapters and labs which prevents students from spending the majority of their time on the WAP standards. The materials lack coherence both within and across courses, presenting standards as isolated, discrete concepts.

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
2/4
+
-
Indicator Rating Details

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.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not meet the expectations that the materials attend to the full intent of the modeling process when applied to the modeling standards. For this indicator, materials were examined for evidence of modeling; however, very few tasks attempted to use the modeling process. Certain tasks, specifically those in the Pull It All Together sections, are designed to provide students an opportunity to experience the full modeling process; yet, the majority of these tasks include a "Task Description" which provides leading questions that take away from the students experiencing the full depth of the modeling process. Overall, only a few tasks incorporated the full intent of the modeling process.

  • Many of the modeling tasks include heavy scaffolding.
    • The scenarios and the tasks are an attempt at meeting the expectation of the modeling standards; however, students are given too much “prompting” towards a method for solving the task. For example, Mathematics I, chapter 2 Pull It All Together asks students to use a table and an equation to compare the growth of two blogs, then proceeds to tell the students how to solve the task. Tasks of this nature take away from the student's ability to begin formulating a plan for solving, the second step in the modeling process.
  • Modeling tasks often do not give opportunities for students to make their own connections.
    • Mathematics II, chapter 9 Pull It All Together offers students an opportunity to use geometry to model a plot of land. Unfortunately, the shape is pre-imposed onto a coordinate grid, and students are not given the opportunity to make that decision on their own, thus deterring from the full modeling process.
  • The following three tasks incorporated the full intent of the modeling process.
    • Mathematics II, chapter 12 Pull It All Together
    • Mathematics II, chapter 13 Pull It All Together
    • Mathematics II, chapter 5 Pull It All Together

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

The 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.
1/2
+
-
Indicator Rating Details

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.

Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
2/4
+
-
Indicator Rating Details

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.
 
Chapter Name Mathematics I Mathematics II Mathematics III
Reasoning and Proof Chapter 10 Chapter 1  
Proving Theorems about Lines and Angles Chapter 11 Chapter 2  
Congruent Triangles Chapter 12 Chapter 3  
Proving Theorems about Triangles Chapter 13 Chapter 4  
Proving Theorems about Quadrilaterals Chapter 14 Chapter 5  
Connecting Algebra and Geometry Chapter 9   Chapter 11
Circles   Chapter 8 Chapter 12
Sequences and Series   Chapter 15 Chapter 9

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.

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
1/2
+
-
Indicator Rating Details

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.

Indicator 1d

The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not meet the expectations that the materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the standards. For this indicator, materials were examined for evidence of coherence both within and across courses throughout the series; however, minimal evidence of coherence was found.

  • The order in which the chapters are arranged lacks a structure that leads to coherence
    • Mathematics I, Chapters 1-5 begin with the topics: solving of equations and inequalities, functions and function notation, systems of equations, etc. Chapter 6 jumps into data analysis and chapter 7 then begins a series of geometry curriculum. Chapter 9 is titled "Connecting Algebra and Geometry" yet the only connections in the chapter are using coordinates to define and create geometric figures. Lesson 9.4 is the only section in chapter 9 that could show this coherence, yet the connection is never pointed out for students. Students do learn to use slope to describe parallel and perpendicular lines; however, the "connections" between Algebra and Geometry are extremely weak and sporadic.
    • Mathematics II, Chapters 1-9 are focused around Geometry standards, the first five of which are duplicated from the Mathematics I book. Then, chapter 10 deals with properties of exponents and switches back to Algebra standards. Chapters 11 and 12 go on to discuss polynomial functions and quadratic functions, and then chapter 13 switches gears and focuses on probability. Chapter 14 returns back to other types of functions, and then the book concludes with sequences and series.
    • Mathematics III: The materials include three duplicated Geometry chapters tacked on to the end. Mathematics III materials missed the opportunity to extend previous knowledge of geometric transformations to transformations of functions. In Lesson 2.4 translation is defined; however, this lesson does not mention the concept of geometric transformation that students have previously studied.
  • As already stated, there are a number of duplicated chapters between the three courses in the series. These repeated sections are a missed opportunity for concept development and connection rather than complete duplication. If there is a need to present the same materials twice, this could have been an opportunity to present the standards from a different perspective.
  • Pull it all Together questions are one opportunity per chapter where students are exposed to the coherence between the standards within that one chapter. Pull it all Together questions help students make connections within and across standards visible, however students should be provided these opportunities throughout the chapter.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not meet the expectations that the materials explicitly identify and build on knowledge from Grades 6-8 to the high school standards. For this indicator, materials were examined for evidence of places where Grade 6-8 standards were expanded on in order to provide students the necessary bridge between prior knowledge and the high school standards. Overall, the Grade 6-8 standards are not explicitly stated, and these standards are presented as if they were high school standards. These standards are never clearly identified as middle school standards, and when they are present they are taught as new lessons rather than reviewed.

  • Some introductory activities have been designed to allow students to pull from previous learning and use a middle grades approach to solving a problem before learning the high school content that makes the problems more manageable, but this is not stated in the materials.
  • Some sections list both high school standards being addressed as well as high school standards for which the section is preparing students.
  • Reference to Grade 6-8 standards is not made in the materials, even though there are numerous sections that clearly address middle grades standards. When present, the included Grade 6-8 content is presented as if the concept is entirely new to the student and does not build on the knowledge from Grade 6-8 standards to the high school standards. For example, Chapter 1 of the Mathematics I book is comprised solely of middle school standards. Lessons 1.1 presents the Distributive Property, lessons 1.2 – 1.4 instruct students on solving multi-step equations, and lesson 1.5 is purely unit conversions and unit rates.
  • The materials fail to link prior knowledge from middle school to current learning. For example, in Mathematics I students are retaught the Pythagorean theorem. In Mathematics III, the materials provide students with the law of cosines, then show the derivation of that law. This was a missed opportunity to connect the Pythagorean theorem to the law of cosines.

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.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Pearson Integrated High School Mathematics Program do not clearly identify the plus standards, when included, and they do not coherently support the mathematics which all students should study in order to be college and career ready.

  • Plus standards are sporadically addressed throughout the materials. Little emphasis is placed on these standards, rather it is as if students are simply exposed to the concepts. There is no evidence that students are experiencing the full depth of the plus standards throughout the materials.
  • The "Implementing the Common Core State Standards" guidebook is the only place that clearly labels the plus standards and states that the + indicates additional mathematics that students should learn in order to advance to higher-level mathematics courses. The materials address some of the plus standards, including N-CN.3, N-CN.4, N-CN.5, N-CN.6, N-CN.8, N-CN.9, A-APR.5, A-REI.9, G-SRT.9, G-SRT.10, and G-SRT.11.
  • There is no evidence of plus standards being identified in either the TE or SE. The front matter of the TE includes a Common Core Standards Table and a Course Pacing Guide which states each lesson and Standard(s) addressed in it; however, the + is not included. For example, Mathematics III, Lesson 12.4 and 12.5 both list G-C.4 but do not properly label it as a plus standard. Because plus standards are not labeled as such, there is no explicit connection between the non-plus and the plus standards.
  • Mathematics III, Lesson 4.8 attempts to address the plus standard A-APR.5. This lesson does "apply the binomial theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle." This lesson, however, focuses more on Pascal's triangle than the application of the binomial theorem. Thus, students are only minimally exposed to this plus standard.
  • Mathematics III, Lesson 4.6 is identified as addressing the standard N-CN.8; however, no evidence of this standard was found.

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2a - 2d

Rigor and Balance: 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; procedural skill and fluency; and engaging applications.

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
N/A

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
N/A

Indicator 2c

Attention to Applications: The 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.
N/A

Indicator 2d

Balance: 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.
N/A

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

Indicator 2e

The 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.
N/A

Indicator 2f

The 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.
N/A

Indicator 2g

The 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.
N/A

Indicator 2h

The 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.
N/A

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

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

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
N/A

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

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

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners.
N/A

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
N/A

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
abc123

Additional Publication Details

Report Published Date: 06/01/2016

Report Edition: 2014

Title ISBN Edition Publisher Year
9780133234503
9780133234510
9780133234541
9780133234558
9780133234572
9780133234589
9780133234619
9780133234626
9780133234695
9780133234701
9780133234770
9780133234794
9780133234978
9780133281101

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. 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).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, 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.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric 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.

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