Alignment

Focus & Coherence

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Rigor & Mathematical Practices

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Meets Expectations
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Does not Meet Expectations
Usability

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Alignment

The instructional materials reviewed for the CPM Traditional series meet expectations for alignment to the CCSSM for high school. The materials meet the expectations for focus and coherence and attend to the full intent of the mathematical content standards. The materials also attend fully to the modeling process when applied to the modeling standards. The materials also meet the expectations for rigor and the Mathematical Practices as they reflect the balances in the Standards and help students meet the Standards’ rigorous expectations and meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

GATEWAY ONE

Focus & Coherence

MEETS EXPECTATIONS

Criterion 1a-1f

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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).

The instructional materials reviewed for the High School CPM Traditional series meet the expectation for focusing on the non-plus standards of the CCSSM and exhibiting coherence within and across courses that is consistent with a logical structure of mathematics. Overall, the instructional series attends to the full intent of the non-plus standards and the modeling process, spends a majority of time on the widely applicable prerequisites from the CCSSM, and requires students to engage at a level of sophistication appropriate to high school.

Indicator 1a

The materials focus on the high school standards.*

4/4
Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials attend to the full intent of the mathematical content contained in the high school standards for all students. For this indicator, all lessons were examined for evidence of each standards presence and the extent to which the full depth was met. Overall, all of the standards are addressed at some point during the course of this high school series.

  • Many of the standards were addressed to their full depth in the instructional material. For example, the Statistics and Probability standards were represented throughout the series. This series places the S-CP cluster in Geometry. The S-ID cluster is in the Algebra 1 text, and the S-IC cluster is in Algebra 2.
    • For example, chapters 6, 10 and 11 of Algebra 1 teach all the standards in the S-ID cluster. Students collect data and model with mathematics as they are learning to quantify variability and describe associations, using common sense, residuals and statistics to interpret categorical and quantitative data.
  • N-Q.1 is partially addressed in the materials. There are questions and activities where units were used which included interpreting units associated with graphs. However, students were not required to use units as a guide to solving all problems, nor were they required to interpret the origin in all data displays.
  • F-IF.2 is partially addressed in that students use function notation and evaluate functions for the inputs in their domains. However, there were no questions or activities found such that students interpret statements that use function notation in terms of a context.
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Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials attend to the full intent of the modeling process when applied to the modeling standards. Modeling standards are well-integrated throughout the entire series. Overall the modeling process is used to reach the full depth of the modeling standards. Furthermore, the materials provide students guided support as they develop their understanding of the modeling process.

  • The first problem in many lessons is a real-world modeling question. The lesson then develops by investigating several aspects related to the modeling content standard. The lesson scaffolds the modeling problem to provide additional support for students to work through the modeling process. For example, in Algebra 2, section 2.1.1 begins with a modeling problem involving a disk and its radius and mass. Problem 2-1 provides scaffolding to help students breakdown the steps necessary to solve the problem. Building on this, problems 2-2 and 2-3 provide extensions to the original modeling problem.
  • The modeling process and every listed modeling standard was evident in the materials. Some examples include:
    • The Burning Candle problem, 11-74, in Algebra 1, section 11.3.1, asks students to gather data and make a prediction using best-fit lines. This is an example of standards S-ID.1 and S-ID.6
    • The Line Factory Logo problem, 2-88, in Algebra 1 asks students to model a logo design and then to have other students use the model to recreate the design. This is an example of modeling standard F-LE.2.
    • The Down on the Farm problem, 2-75, in Algebra 1 asks students to use multiple representations to model the weight of chickens since they were hatched. This is an example representing many standards: N-Q.2, A-CED.2, F-IF.4, F-IF.6, F-IF.7.A, F-BF.1.A, F-LE.1.B, F-LE.2, and F-LE.5.
    • The Sandy Dandy Dune Buggies problem found in Algebra 2 section 4.2.3 models a linear programming situation, including thinking about constraints associated with the situation. This is an example of standards A-CED.3 and F-IF.5.
    • The Blood Splatter problem found in Algebra 2 section 7.1.1 models a swinging pendulum, resulting in a sine curve. This is an example of standard F-TF.5.
    • The Cookie Cutter problem, 8- 115, in Geometry is an authentic, modeling problem in that no specific directions as to what tools, processes, or mathematics should be used are given, yet students must use their knowledge of ratios in Geometry to solve the problem. The standards covered in this problem are G-MG.1 and G-MG.3.
    • The Interior Design problem in Geometry section 7.1.3 models an optimization problem, scaffolding for additional support in problems beyond the original problem. This is an example of standard G-MG.3.
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.

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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.

The Instructional materials reviewed for the High School CPM Traditional series 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).

  • The materials in the teacher's resources suggest a timeline and shows a strong focus on widely applicable prerequisites.
    • In Algebra 1, the majority of the 121- 128 days focus on the widely applicable prerequisites.
    • In Geometry, the majority of the 140 days focus on the widely applicable prerequisites, with 37 of those days spent on optional lessons (lessons that can be omitted depending on students prior geometry knowledge).
    • In Algebra 2, the majority of the 129-134 days focus on the widely applicable prerequisites.
  • The prerequisites from Grades 6 - 8 were not seen as distracting, but as helpful. For example, in Algebra 1, section 1.2.3 includes the Grade 8 standards on functions. This is helpful in building the high school function objectives of the WAPs.
  • Box plots, a middle school learning prerequisite, are found in the Algebra 1 "math notes" in section 11.2.1. The S.ID cluster of standards in Chapter 11 builds on this middle school standard in supporting the statistics and probability standards in the WAPs.
  • In the Review & Preview sections of each lesson in Geometry, there are problems that focus on Algebra standards, reinforcing and continuing to build on these important skills from the WAPs.
2/4
Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.

The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that students are provided with opportunities to work with all high school non-plus standards and do not distract students with prerequisite or additional topics. Lessons were examined for evidence that, when used as designed, they would enable all students to fully learn each standard. Overall, the lessons are structured in a way that students will fully learn all aspects of most standards and do not distract students with prerequisite or additional topics. However, there are a few missed opportunities for students to make every connection and fully learn all aspects of every standard.

  • A-SSE.3.B: There are several instances where the student is asked to complete the square and to find the vertex. In Algebra 1,there are three examples where the question asks if the vertex represents a maximum or minimum value, instead of students completing the square to "reveal" the maximum or minimum value (9-21, 9-76, 10-125).
  • A-APR.3: The lessons call for students to identify x-intercepts and roots but seldom have them "identify zeros" and "use zeros" as stated in the standard. For example, Algebra 2, 8.1.1 (and the remainder of Chapter 8) meets this standard, except that it mainly uses x-intercept's and roots in place of zeros.
  • A-REI.1: Section 3.2.1 of Algebra 1 uses algebra tiles and "legal moves" to solve equations. Problem 3-104 in Algebra 1 asks students to show all of their work in solving the equation. There were limited problems that asked students to "explain each step" or "construct a viable argument."
  • G-C.2: The relationship between central, inscribed and circumscribed angles was not explicit. Specifically, circumscribed angles were only taught as a circle circumscribing a triangle; hence, little depth about the relationships of circumscribed angles was evident. Tangent lines are used frequently, but the term "circumscribed" is not used enough for students to fully learn the concept.
  • G-CO.2: There is no explicit instruction of functions that take points in the plane as inputs and give other points as outputs, but there are problems to solve for students in the homework.
  • G-CO.13: There are questions and activities in which students construct an equilateral triangle and a regular hexagon inscribed in a circle. However, there was only one note of evidence found where students constructed a square inscribed in a circle, and this was in the teacher eBook via a technology link.
  • G-GPE.6: There were only a few problems that partitioned segments in a ratio other than 1:1.
  • F.IF.6 - There was limited evidence found of finding the average rate of change in non-linear situations. Many questions and activities have students calculate and interpret the average rate of change of a function over a specified interval. However, there is a lack of questions and activities where students estimate the rate of change from a graph (2-65 in Algebra 1). In Algebra 2, there are a few exercises (3-55, 6-28) that help students learn this standard. Furthermore, these two specific examples do not ask students to make estimates or interpret the average rate of change.
  • F.IF.9: There were missed opportunities for students to "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)". There were plenty of examples where students used one function to compare multiple representations. However, students were rarely given two different functions and asked to compare their properties.
  • F-IF.4 & F-IF.7.C: Key features are interpreted throughout the series; however, there was little evidence of the actual verbiage of "end behavior" used.
  • In the F-BF and F-IF clusters, using function notation was not as strong as equation notation throughout the entire cluster of standards. Students do have opportunities to do both y = and f(x) = problems; however, given that these clusters are part of the function domain, there is a missed opportunity for function notation to be integrated into the lessons.
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Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials require students to engage in mathematics at a level of sophistication appropriate to high school. Overall, the materials meet the full depth of the non-plus standards and give all students an opportunity to have extensive work with the non-plus standards.

  • Each lesson throughout the series is designed to provide students with "learning and practicing a math skill at spaced intervals" (page 31, Teacher Resource, Team Support & Universal Access). The method of spaced intervals allows students to demonstrate mastery over time and to make connections between concepts.
  • Each course is also designed to allow for students at a variety of learning levels to access and engage with grade-level, non-plus standards. Using the Teacher Resource binders, teachers are provided with a variety of instructional strategies to assist students who may struggle with aspects of the course work (page 32). There are additional suggestions and supports for students who need additional help (page 33), students who are unprepared for the course (page 34), special needs students (page 34 - 35), English Language Learners (page 35 - 36), and advanced learners (page 37).
  • The instructional materials contain a tutorial website for homework help through the eBook. Support is provided for both parents and students who need additional assistance at home. The homework help includes free access via the Internet to all of the Review & Preview problems from the student text. Some of the problems include hints and complete solutions.
  • The materials contain a Literacy Support Guidebook within the Teacher Resource Binders (pages 39-49).
  • Any guidance for differentiation stresses that pacing is the key to success, rather than reducing the concepts to be learned. The pacing in the Teacher Edition is designed for instructing students at grade level. Below-grade-level students should be provided more time with the concepts by "concentrating on the core problems" that "teach sub-skills and the conceptual understanding needed to progress towards mastery of the course objectives" (page 37). Advanced students should complete the challenges (enrichments) and extensions within the latter parts of the lessons, in addition to core problems and homework.
  • Each lesson includes teacher instructions for facilitating discussion around the lesson's core concepts and the connections students have made with other mathematical concepts in earlier coursework.
  • The context of the problems are relevant to high school students. Some examples of high school sophistication include, but are not limited to:
    • Algebra 1: Problem 6-109 requires students to work with a piecewise function, find regression lines using a calculator and discuss residual plots. Students are using both exponential best fit and linear best fit models, and are expected to make predictions and identify domains.
    • Geometry: Sections 2.1.2 and 2.1.4 continue to build on problem 2-14 so that a level of sophistication is developed in a real-life and relevant situation that is appropriate for high school students. Students have ample opportunities throughout Chapter 2 to engage deeply with the CCSSM of G-CO.9 and G-CO.10.
    • Algebra 2: In Chapter 6, problem 6-137 involves a case of the cooling corpse. It is a high school level forensic science problem that is sophisticated in both context and content, involving log modeling, and appropriate for Algebra 2.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation 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. Overall, the materials include connections that are intentional and thoughtful, and they consistently point out places where students are expected to connect their learning to previous lessons. The sequence of the materials is designed to spiral concepts throughout the chapters and courses.

There are several examples of connections made within the books in the series:

  • The homework section within each lesson includes distributed practice of previously learned skills. Each lesson has a Review & Preview section that includes several problems from previous courses and previous lessons.
  • The homework problems allow students to apply previously-learned concepts and skills in new contexts. For example, the Team Challenge problem in section 5.1.4 of Geometry extends the trigonometric application of the Climbing in Yosemite problem introduced as an early problem in 5.1.4, and builds on the lessons taught in sections 5.1.1 and 5.1.2.
  • Throughout the materials, there are checkpoint problems to determine if students have understanding of previous skills at the expected level. For example, problem 2-53 in Algebra 2 asks students to determine the distance between two points and to write an equation for the line between the points. Checkpoint 2A at the end of the Algebra 2 materials provides more problems of this type for students who need more practice of this skill learned in a previous course.
  • Algebra 1 demonstrates strong connections between the conceptual categories of the standards. The materials connect linear functions, exponential functions, arithmetic and geometric sequences, and recursive and explicit representations. In Chapters 1 and 2, students develop a foundational understanding for both the general idea of a function and linear functions. Chapters 3 and 4 focus on solving, simplifying and solving systems of equations but continue to spiral back with problems involving functions and linear functions to deepen and reinforce these foundational skills. In Chapter 5, students begin to work with both arithmetic and geometric sequences which is deliberately connected to students understanding of functions and linear functions. Chapter 5 also builds a foundation for exponential relationships, which is explored more formally in Chapter 7 when exploring and examining geometric sequences. Additionally, the problems use both explicit and recursive representations to further push and connect these concepts.

There are several examples of connections made between the books in the series.

  • One example of this connection exists within Geometry and in the connections between Algebra 1 and Geometry. The Geometry book introduces students to similarity early (Chapter 3) and uses the concept of similarity throughout many of the remaining chapters. Chapter 4 carefully develops the major concepts of trigonometry through similarity and slopes of lines. In fact, students are not presented with the formal tangent function until they have had extensive work exploring and solving trigonometry related problems using only their conceptual understanding of slope, similarity, and proportional reasoning, thus making the connections to key concepts from the Algebra 1 materials and previewing concepts in the Algebra 2 materials.
  • Another specific instance of connections among standards is in Chapter 2 of Algebra 1, when linear relationships are built using slope triangles from Grade 8. This continues in Geometry in lesson 4.1.3 when students connect slope triangles to trigonometric ratios. Then, Algebra 2 continues with slope triangles in 1.1.2 in the "Math Note" section as a review of linear functions.
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Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The instructional materials reviewed for the High School CPM Traditional series partially meet the expectations that the materials explicitly identify and build on knowledge from Grades 6-8 to the High School Standards. Overall, content from Grades 6-8 is present, but it is not always clearly identified and pinpointed to a specific middle school standard.

  • Standards from Grades 6-8 are developed as a natural progression into high school, particularly with ratios, slope, geometry concepts and exponents, but there is no explicit mention of any of the specific middle school standards.
  • The connections between concepts are partially articulated in that the Teacher Resources Planning documents identify information as "in earlier grades," "by the end of eighth grade," and "middle school concepts."
  • The lesson and chapter overviews describe the connections between lessons and future learning but miss the opportunity to explicitly identify the actual middle school standards referred to in these sections. The opening sections of Algebra 1 state that "in previous courses you may have learned...," and then describe the upcoming lesson. There are many other places where the text informally references prior learning "in the previous lessons you learned....". Prior standards are used to support the progression of high school standards, but there is a missed opportunity to explicitly identify the standards.
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.

The instructional materials reviewed for the High School CPM Traditional series explicitly identify the plus standards, when included, and the plus standards coherently support the mathematics which all students should study in order to be college- and career-ready.

  • Most of the plus standards are identified in the teacher notes of the teacher resources. However, the materials offer no guidance or pacing suggestions should teachers not wish to use the plus standards. Because of the highly connected and cyclical nature of this book, it could be difficult to decide how to not include the plus standards.
    • One instance of a missed opportunity of identifying lesson problems as plus standards, or extra topics, is in section 5.1.3 of Algebra 2. Composition of functions is referred to in F-BF.4b. This concept is presented in a way that connects to, and enhances, students understanding of inverses and logarithms. However, because the plus standard is not explicitly identified, it is not clear when problems go above and beyond the non-plus standards.
  • There is no evidence or reference to the plus standards in the student materials.
  • Work with the plus standards does not deter from the work with the non-plus standards.
  • In the Algebra 2 teacher resources, the quarterly benchmarks identify plus and non-plus standards that are appropriate to assess in each quarter of the course.
  • While the sequencing for plus standards is not explicit, the sections that include the plus standards meaningfully connect to, and enhance, the non-plus standards. The plus standards that are identified are addressed to reach the full depth of the standard. For example:
    • A-APR.7: In Sections 3.2.2 - 3.2.5 of Algebra 2, the standard is in a math note in Chapter 3 and has more practice problems for fluency in checkpoints 6A and 6B.
    • G-SRT.10, G-SRT.11: Sections 5.2 and 5.3 of Geometry address the Laws of Sines and Cosines. Each is fully developed in this chapter titled "Completing the Triangle Toolkit," which begins with extending students understanding of trigonometric ratios.

GATEWAY TWO

Rigor And Mathematical Practices

MEETS EXPECTATIONS

Rigor and Balance
MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, all three elements of rigor are thoroughly attended to and interwoven in a way that focuses on the needs of a specific standard as well as balancing procedural skill and fluency, application and conceptual understanding.

Criterion 2a-2d

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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.

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters. Overall, the clusters and standards that specifically relate to conceptual understandings are thoroughly addressed. The materials develop conceptual understandings across the series by building on a tactile form.

  • Most of the lessons across the series are exploratory in nature and encourage students to develop understanding through questioning and activities.
  • Each chapter has a closure section that recaps the concepts of the chapter. It includes reflections on and synthesis of the connections to what the learning targets were for the chapter.
  • A-REI.10 addresses conceptual understanding, and the materials offer opportunities for students to develop a deep understanding and ability to communicate or demonstrate that understanding of A-REI.10. Sections 10.3.1 and 10.3.2 in Algebra 1 and section 4.1.2 in Algebra 2 explore this standard at length, guiding students to make predictions, solve in multiple ways, and explain intersections and intercepts of graphs. The Review & Preview sections of each course spiral this concept throughout the series for all types of functions (i.e., linear, polynomial, rational, absolute value, exponential and logarithmic as stated in the standards).
  • Multiple representations are embedded throughout the series, reinforcing students' ability to verbalize and recognize connections graphically, analytically, and numerically. Algebra 1 begins building multiple representations in section 1.1.4, and Algebra 2 frames this again starting in chapter 2. Multiple representations continue throughout the remainder of the materials to draw connections among parent graphs from all types of functions. Additionally, the materials use a common resource called a representation web to reinforce four ways to look at functions.
  • Conceptual understanding is a strength of this series. Concepts grow over many lessons within and between each course in the series. Specific clusters and domains that are represented include N-RN.1, A-APR.B, A-REI.A, A-REI.10, A-REI.11, F-IF.A, F-LE.1, S-ID.7, G-SRT.2 and G-SRT.6. Some specific examples are:
    • A-APR.A: Students use algebra tiles to build conceptual understanding of adding, subtracting, and multiplying polynomials beginning in Chapter 3 of Algebra 1. Students make connections between the tactile and the algebraic methods of performing arithmetic operations on polynomials by moving from algebra tiles to generic rectangles to algebraic computation. In lesson 3.2.3, students are specifically told what is meant by "a closed set" and asked to explore if integers are closed under addition given that whole numbers are closed under addition. Then, they explore and explain whether polynomials are closed under addition and subtraction, extrapolating from what they know about whole numbers and integers.
    • F-TF.A: In Chapter 7 of Algebra 2 a conceptual model is used to develop the concept of a unit circle, radian measures, and trigonometric functions. First, students are introduced to models for cyclic relationships through an experiment in 7.1.1. Then, in 7.1.2 students create a sine graph using experimental data based on a Ferris wheel. In the following lesson, students use the same Ferris wheel to develop a unit circle and discover reference angles at various points on the circle and their relationships to each other. In lesson 7.1.4, students create a cosine function and calculate horizontal distances in a unit circle to draw conclusions about relationships between sine and cosine and their functions. The next lesson introduces students to radian measures. All of this leads to the conceptual understanding in 7.1.6 in which they use radian measures to determine the exact values of the coordinates on a unit circle.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters. The clusters and standards that specifically relate to procedural skills and fluencies are thoroughly addressed multiple times. The materials develop procedural skills and fluencies across the series.

  • Checkpoints are scattered throughout the lessons in the series. The checkpoints are designed as fluency problems. If students work through a checkpoint and see that they are not fluent with that problem, then there are more problems at the back of each of the student editions that provide more practice for students to work through until they reach fluency.
  • The spaced nature of the problems helps build the fluency since students are expected to know how to solve them 'on demand' and not just after the section on that standard.
  • Examples of select cluster(s) or standard(s) that specifically relate to procedural skill and fluency include, but are not limited to:
    • A-APR.1: There are many opportunities to develop procedural fluency with operations of polynomials in Algebra 1 Chapter 3 and again in Algebra 2 in section 3.1. Additionally, there are checkpoints in the reference section of each series that address this standard. These checkpoints include 6B in Algebra 1, 5A in Geometry and 5A in Algebra 2.
    • A-APR.6: There are many opportunities to develop procedural fluency in rewriting simple rational expressions in Chapter 8 of Algebra 2. Additionally, there is Polydoku (similar to Sudoku) and checkpoints 6A and 6B add to the already present opportunities throughout Chapter 8, and the following chapters.
    • F-BF.3: Effects of parameters of functions is found throughout the Algebra 1 course, and again in chapter 2 of Algebra 2. There is lots of practice throughout both books and as spaced practice in Geometry.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that 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. The cluster(s) or standard(s) that specifically relate to applications are thoroughly addressed multiple times. The materials include numerous applications across the series.

  • In every lesson, students are solving non-routine problems, from simple to complex. Students are provided opportunities to make their own assumptions, question, investigate, critically analyze and communicate their thinking in groups, independently and in learning logs as they model mathematical situations.
  • The lessons are built upon application and modeling problems. The lessons do not show several, worked examples of various problems followed by a set of problems where subsets align to each type of the worked examples.
  • Modeling builds across high school courses, with applications that are relatively simple when students are first encountering new content. For example, Algebra 1 problem 1-38 has students recall patterns, a tool that students have been learning since elementary school, and begins teaching families of functions. Families of functions are then developed throughout the series. This is an example of a problem that provides opportunities for students to make their own assumptions in order to model a situation mathematically. Students must reason about what happens as the pattern continues, thus beginning early in the series to challenge themselves in making assumptions.
  • Examples of select cluster(s) or standard(s) that specifically relate to applications include, but are not limited to:
    • F-IF.7a: The Saint Louis Gateway Arch in 9.1.3 in Algebra 1.
    • G-SRT.8: Statue of Liberty problem in 4-45 and 4-46; Wheelchair Ramp problem in 5-24.
    • S-IC.1: Charity Race in 9.3.2 of Algebra 2; ACT Scores in 9.3.3 of Algebra 2.
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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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that 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. Overall, there is clear evidence of all three aspects of rigor present in the materials. Additionally, the materials engage in multiple aspects of rigor in order to develop students’ mathematical understanding of a single topic/unit of study.

  • Fluency is specifically targeted in the Checkpoint problems and also in the spaced practice.
  • Concepts are systemically developed in the lessons and are intentionally reinforced in the closure activities. The closure at the end of each section and the spaced nature of the homework intentionally connects conceptual learning with problem solving and procedural fluency.
  • Most lessons start out with an application or investigation. For example, Algebra 2, section 7.2.1 begins with students investigating functions and Algebra 2, section 7.1.2 begins with students engaged in an application, the roller coaster problem.
  • The Review & Preview sections of each lesson also intentionally interweave problems of all three types of rigor together.
  • As an example of this balance, Chapter 2 in Algebra 1 focuses on linear relationships. The first two lessons use investigations of tile patterns with various representations to introduce and develop conceptual understanding of linear relationships. The third lesson has students investigating "steepness" using a variety of representations. Finally, in the fourth lesson, these explorations are formalized with mathematical definitions for slope and slope-intercept form of a line. In the remaining five lessons of the chapter, students apply this understanding to a variety of real-world situations and contextual problems that further develop connections and lead to procedural fluency.
  • As another example, Chapter 4 in Geometry maintains this balance in a different way. The first lesson begins with a real-world investigation of the relationship between angles in right triangles and the ratios of side lengths. The next two lessons use conceptual understanding to solve basic problems and develop procedural fluency, even though the students do not have the formal understanding of a tangent function. In lesson 4, the investigation culminates in the formal tangent function with additional procedural practice. Then lesson 5 provides a variety of real-world problems to apply the conceptual understanding and procedural fluency. Chapter 5 follows a similar pattern to introduce students to sine and cosine functions, Pythagorean Theorem, and a wide variety of problems involving triangles.

Mathematical Practice-Content Connections
MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of all eight MPs, in connection to the high school content standards. Overall, many of the lessons in the series deliberately incorporate the MPs as an integral part of the learning. Each book has a "correlation" document showing sample specific lessons that integrate various practices standards. The teacher's notes list the specific MPs that are a focus for each lesson. These are identified in a shortened form (i.e., attend to precision), but there is not a number attached. Teachers are encouraged to discuss the MPs with the students "to clarify what the Standards for Mathematical Practice are and to see how they connect to the work the students are doing." Each chapter in the student materials begin with identifying an MP in the guiding question. The teacher's resource guide emphasizes these practices by encouraging teachers to spend an appropriate amount of time on each of the appropriate MPs. The full practices are printed as a reference in the student textbooks and are part of what students are expected to integrate into all they do.

Criterion 2e-2h

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

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of making sense of problems and persevering in solving them as well as attending to precision (MP1 and MP6), in connection to the high school content standards. Overall, the majority of the time MP1 and MP6 are used to enrich the mathematical content and are not treated as individual mathematical practices. Throughout the materials, students are expected to make sense of problems and persevere in solving them while attending to precision. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

  • There was no evidence of instances where MP1 and MP6 are treated as separate from the mathematics content throughout the series. Many lessons require students to "make sense" of problems and "persevere" when solving them. Students are constantly asked to explain or compare representations or solutions paths, hence a natural opportunity to practice precision.
  • Students are encouraged to persevere and attend to precision as they reflect on and correct their assessments. They may partner together to discuss mistakes and revise their work. Students are asked questions like: Why did you miss the problem? What did you learn from revising the problem? Who (if anyone) helped you and what did they say to help you better understand the problem? Make up a new, similar problem to show and explain to a new student (in writing) how to solve the problem. Analyzing errors in thinking or computations incorporates many of the MPs.
  • It is important to note that MP1 and MP6 are represented in many lessons and assessments throughout the series. Listed below are a few examples of where MP1 and MP6 are used to enrich the mathematical content:
    • In Algebra 1, section 2.2.3, a challenging team puzzle is incorporated into the lesson that encourages making sense of problems and persevering in problem solving and attending to precision as part of the solving of this puzzle.
    • Geometry, section 8.3.3, includes 4 core problems, of which 3 are recommended for students to make sense of the problems and persevere in solving them as well as attending to precision while solving the problems. This particular lesson is an extended lesson, designed so that students have extra time to read, interpret, strategize, engage in the problem solving, and solve the problems, attending to these specific mathematics practices.
    • Algebra 2, section 8.1.3, includes opportunities for students to use these math practices as they are making connections and discoveries about higher level polynomial functions. They are given opportunities to check their answers with multiple methods and monitor and evaluate their progress in solving problems as they persevere in solving problems.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of reasoning and explaining (MP2 and MP3), in connection to the high school content standards, as required by the MPs. Overall, the majority of the time MP2 and MP3 are used to enrich the mathematical content and are not treated as individual practices. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

  • Many lessons require students to "reason abstractly and quantitatively" and "construct viable arguments and critique the reasoning of others." Students are constantly asked to represent situations symbolically, create their own conjectures, determine if their answers make sense, and communicate this in various ways, hence a natural opportunity to engage in these two mathematical practices.
  • It is important to note that MP2 and MP3 are represented in many of the lessons and assessments throughout the series. Listed below are a few examples of where MP2 and MP3 are used to enrich the mathematical content:
    • The Chapter 7 sample chapter test in Algebra 1 has five problems. These five problems are representative of problems taught in that course. This particular sample test requires students to explain, justify, show or provide evidence for all five problems on the test. Most of the problems also require students to represent the situations symbolically and to understand the relationships between problem scenarios and mathematical representations. One specific problem asks students to determine if their answer makes sense.
    • The teacher's notes of section 6.1.2 in Geometry lists at least five different probing and clarifying questions as a guide for the teacher to help students who may be struggling at different parts of the lesson. Teachers are encouraged to use this questioning strategy in connection to MP2 and MP3 to enrich the mathematics content. For example, one of the questions, "Is SSA a valid similarity conjecture? Why or Why not?" helps students to construct viable arguments as they are learning about and understanding similarity and congruence of triangles.
    • Chapter 2 of Algebra 1 focuses on helping students move between real world situations, graphs, tables, and equations. In doing this, students begin to reason abstractly and represent situations symbolically. The chapter also asks students to move in the other direction, giving them an equation or graph and asking them to contextualize the abstract representations. This is the essence of MP2 and the materials provide ample opportunity to develop this type of thinking. This chapter also has students creating and critiquing arguments. Some examples of where students are asked to justify or create arguments to support their answers are problems 2-1, 2-9, 2-12, 2-13, 2-14, 2-23, 2-26, 2-28, 2-31, 2-32, 2-35, 2-53, 2-54, 2-68, 2-69, 2-74, 2-77, 2-78, 2-80, 2-87 and 2-96. Some examples of where students are asked to critique the reasoning of others are problems 2-18, 2-25, 2-38, 2-43 and 2-97.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of addressing mathematical modeling and using tools (MP4 and MP5), in connection to the high school content standards, as required by the MP. Overall, the majority of the time MP4 and MP5 are used to enrich the mathematical content and are not treated as individual practices. Throughout the materials, students are expected to model with mathematics and use tools strategically. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

  • Many lessons require students to "model with mathematics" and "use appropriate tools strategically." The modeling is done with multiple representations and using various tools. Digital resources, calculators, algebra tiles, blocks, graph paper, and various other tools are used throughout the series. Students are not told which tools to use in solving problems.
    • For example, in sections 7.1.1 - 7.1.2 of Algebra 2, students use tools to build their own models/tools to investigate cyclical behavior. In section 5.1.3 of Algebra 1, students use measuring tools, coordinate grids, and technology to model exponential decay. There are many times when students use tools in smaller, non-modeling situations such as homework problems or investigations and ample opportunities for students to use tools strategically in full, modeling situations.
  • It is important to note that MP4 and MP5 are represented in many of the lessons and assessments throughout the series. Listed below are a few examples of where MP4 and MP5 are used to enrich the mathematical content:
    • In section 9.1.3 of Geometry, students are encouraged to make use of appropriate tools as they engage with investigating solids. The teacher's resources recommend a few tools and manipulatives to have available for use. This same lesson has students use graph paper to create and use a model involving a net and a solid that has multiple solutions. Additionally, students solve problems applying prior knowledge to new problems. Students make assumptions and reason if those assumptions work with additional solid figures, leading to drawing conclusions pertaining to surface area and volume of solids.
    • Technology is extensively used across the series. Many lessons and problems are linked to Desmos.com to investigate patterns or connections between graphs and equations or to work with data in modeling situations.
2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that materials support the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards, as required by the MP. Overall, the majority of the time MP7 and MP8 are used to enrich the mathematical content and are not treated as individual practices. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

  • Since students are developing contextual understanding in most lessons, the units often bring closure in asking students to generalize and make use of structure in their closure sections.
  • Students are constantly extending the structures used when solving problems that build on one another and, as a result, are able to solve increasingly complex problems. Repeated reasoning allows for increasingly complex mathematical concepts to be developed from simpler ones, and this series has the expectation that this will occur.
  • It is important to note that MP7 and MP8 are represented in many of the lessons and assessments throughout the series. Listed below are a few examples of where MP7 and MP8 are used to enrich the mathematical content.
    • In lesson 5.3.1 and 5.3.2 of Algebra 1, students are asked to compare growth rates in tables to explore the structure of linear and exponential equations and to differentiate between them. They then use their observations to make generalizations about linear and exponential equations to create equations from data tables.
    • In Chapter 5 of Geometry, students use what they know about similarity to develop definitions for sine and cosine functions. Then they further use the structure of similarity and trigonometry to generalize the relationship between angles and sides of triangles by creating shortcuts for special right triangles.
    • In section 2.1.3 of Algebra 2, the lesson calls for students to use their prior knowledge of quadratics and parabolas to go to greater depths by prompting students to look at patterns and structures of quadratic equations to make more generalizations than have occurred prior to this lesson. Though students are not directly asked to decompose "complicated" things to "simpler" things, this is something that students may discover through the investigation in the lesson. One of the main goals of the lesson is to be able to quickly graph and identify key parts of a graph based on an algebraic representation, without a graphing calculator. In essence, students are looking for shortcuts and general methods to do this as these processes are repeated.

GATEWAY THREE

Usability

MEETS EXPECTATIONS

Use and design facilitate student learning
MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials are designed well and take into account effective lesson structure and pacing. The design and layout of the materials, in print and in the eBook, are quite simple, easy to use and not distracting. In addition the consistent structure of each lesson, homework set including the Review & Preview sections and chapter closure section help to make students comfortable and confident with the lessons.

Criterion 3a-3e

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

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. Students are learning new mathematics in each lesson and then applying what they have learned in order to build knowledge. The spaced and spiraling nature of the series helps build mastery. Each chapter, section, and lesson has a variety of problems and exercises, and has intentional purpose in developing learning and thinking.

2/2
Indicator 3b

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. The materials encourage fluency through their spaced homework, helping students retain and apply new learning throughout the series. Rote procedural exercises are present, but not in mass quantities. The exercises are given in intentional sequences.

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that students are asked to produce a variety of products during each lesson in each chapter to demonstrate their learning. The series continuously asks students to produce models, practice fluency, create arguments, justify their answers, attend to mathematical practices and make real-world connections. This is done through homework, closure reflections, portfolios, team tasks, explanations, models, arguments (with stop light problems using error analysis), learning logs, cumulative assessments, checkpoint problems and journal entries.

2/2
Indicator 3d

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. Each chapter in each textbook contains teacher notes in the chapter introduction that provides clarity on the lesson design and intent and a suggested assessment plan. For example Algebra 2, chapter 4 says "This chapter begins with a focus on two ways to solve equations and systems of equations: algebraically and graphically. You will build on your understanding of solving and solutions from previous courses to gain a broader and stronger understanding of the meaning of solutions. In Section 4.2, you will expand your understanding of solving and solutions to include inequalities. You will solve problems designed to illustrate how inequalities might be used for more complicated applications."

The series makes use of a wide range of virtual manipulatives. The materials have their own collection of virtual manipulatives including algebra tiles, base ten blocks, probability tools, data representation tools, transformation tools, similarity toolkit, numbers lines and graphing tools. The materials also make regular use of premade Desmos.com graphs and other applets. There are general manipulatives and tools that the materials recommend always having available. A few examples of these include, but are not limited to colored pencils, graph paper, markers, masking tape, meter sticks, rulers, scissors, and tape. Then, there are specific manipulatives and tools that will be needed for specific lessons. A few examples of these include, but are not limited to rope, foil pans, bouncy balls, candles, calculator-based rangers, digital scales and yo-yo's.

Indicator 3e

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the visual design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. The design and layout of the materials, in print and in the eBook, are quite simple, easy to use and not distracting. The structure of the lessons and layout of the textbook in black and white help students focus on mathematics and eliminate distractions.

Teacher Planning and Learning for Success with CCSS
MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teacher learning and understanding of the standards. Overall, the materials provide the teacher necessary supports using adult-level expectations and the student with guiding questions for appropriate mathematical development and the parents with resources.

Criterion 3f-3l

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

2/2
Indicator 3f

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. In many sections of the student materials, the leading paragraph of the lesson begins by listing three to four questions, then asks students to use these questions to guide the work in the lesson. In addition, the teacher resources provide teachers with guiding questions for the teacher to use when circulating the room. For example, in the teacher notes for section 3.1.1 in Algebra 1 the teacher is given the following: "As you circulate, ask questions that require students to justify their patterns or that encourage students to look for patterns, such as, “What is the exponent of the result? How is that related to the original problem?” and “How can you convince me that your shortcut works?" There are additional questions later in the teacher resources that are listed as useful questions for other parts of the lesson.

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Each lesson has a full printed write-up to explain the content and instructional goals as well as a video with the same purpose. Each lesson also describes how to use the supporting technology as well as how to run the lesson if technology is not available. There is a TI-83 student and teacher guide included. For example, the eBook teacher notes for the opening of Chapter 7 in Geometry includes overview paragraphs, guiding questions, a chapter outline, a teacher guide video, Smart Board file, discussion on the Standards for Mathematical Practices, a "Where's it Going?" paragraph, and a suggested assessment plan.

2/2
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.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials contain adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject. Lesson videos and lesson teacher notes (both printed and in the eBook) provide teachers with a full preparation for each lesson, including historical notes, video models, mathematical background and adult-level explanations to guide the teacher. The series provides a newsletter with lesson ideas and up-to-date strategies and best practices to guide teachers in planning and in advanced learning of the mathematics. Past editions of the newsletter are archived in the teacher support of the teacher materials.

1/2
Indicator 3i

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

The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials explain the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve. The series makes vague reference to future and past learning but does not give clear, precise information about how current content fits into the vertical progression of learning. There is an accelerated pacing guide for Grades 7 and 8 but no other progression information of the overall mathematics curriculum for Kindergarten through Grade 12.

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).

The instructional materials reviewed for the High School CPM Traditional series provide a list of lessons, cross-referencing the standards covered. The materials in the series provide several different pacing guides, lesson sequences, and standards (both practice and content) correlations. Additionally, the materials include a quarterly benchmarks correlation that includes plus and non-plus standards.

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.

The instruction materials reviewed for the High School CPM Traditional series have an ancillary resource book for each course designed to provide parents with additional practice problems for students, including explanations for parents.

In the student resources, each lesson begins with a learning objective written for students. The lesson objectives for students are written in a way that help students make connections to previous learning concepts or experiences and to real-world contexts when appropriate. While the standards for the lesson are not explicitly written in the student text, the lesson objective is clear and aligned to the CCSSM. For example, the objective for students from Algebra I lesson 9.1.2 reads, "In the previous lesson you developed methods to solve quadratic equations. Today you will learn a new method to solve them." This lesson objective directly aligns to A-REI.4.

Indicator 3l

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

The instructional materials reviewed for the High School CPM Traditional series provide many different instructional strategies, support on how to effectively implement these strategies and extensive research literature supporting the use of these strategies and the design of the materials.

There is an extensive research summary including research on problem based learning, mixed spaced homework, and cooperative learning found in the web-based teacher edition under the teacher tab. There is also a tab with teaching strategies included under the same teacher tab.

Assessment
PARTIALLY MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials offer teachers resources and tools to collect ongoing data about student progress on the standards. The materials provide assessments that not only offer evidence of students’ knowledge of the CCSSM, but also elicit evidence of the students' knowledge of the MP. Unfortunately, there is a missed opportunity in identifying the specific standards that align to each of the assessment items. Additionally, there are limited strategies for gathering information about students’ prior knowledge.

Criterion 3m-3q

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

1/2
Indicator 3m

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

The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials provide strategies for gathering information about students' prior knowledge within and across grade levels. The materials have pre-assessments for Algebra 1. There was no indication of what to do with the information that is assessing prior knowledge from previous courses or information pinpointing standards that are being assessed. The materials do provide the opportunity within lessons to see prior knowledge being addressed.

2/2
Indicator 3n

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide strategies for teachers to identify and address common student errors and misconceptions. The stoplight problems provide opportunities for students to find errors and critique reasoning. The teacher notes also provide tips for teachers to address common errors. The closure sections provide opportunities for discussion of common errors and misconceptions, along with the cooperative learning tasks.

2/2
Indicator 3o

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The teacher materials provide rubrics along with information on giving feedback on portfolios, team tests, presentations and participation quizzes. Students also have feedback available through the eBook homework help and the animated explanations.

Every lesson has a Review & Preview section. In this section, there are homework helps that are hyperlinked to selected hints, answers and e-tools to help provide feedback to students on skills and concepts. This part of each lesson reviews problems from past learning objectives, chapters and courses within the series. One example is in section 4.1.3 of Geometry where students work 6 problems from previous chapters in Geometry.

Indicator 3p

Materials offer ongoing assessments:

0/2
Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for the High School CPM Traditional series do not meet the expectation that assessments clearly denote which standards are being emphasized. No standards are denoted on either the printed or sample digital assessments that were provided.

1/2
Indicator 3p.ii

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

The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The materials in the series offer ongoing formative and summative assessments. The assessments include some generic rubrics. However, the rubrics are typically very general in nature and may not provide enough guidance to teachers to interpret current student performance. Assessments have answer keys but lack any guidance to the teacher on how to score or how to interpret the results.

Indicator 3q

Materials encourage students to monitor their own progress.

The materials in the series encourage students to monitor their own progress through learning logs, concept webs, closure, team activities and portfolios.

In the assessment tab of the teacher resources for each book in the series the following is provided: "Teachers require students not only to revise their incorrect solutions, but also to analyze the errors in their thinking or computations by answering a series of questions. Some examples are:

  • Why did you miss the problem? (Careless error, did not know how to do it, guessed, used the wrong formula, tried a strategy inappropriate for the problem, etc.)
  • What did you learn from revising the problem?
  • Who (if anyone) helped you and what did they say to help you better understand the problem? Please be specific.
  • Make up a new, similar problem. Show and explain to a new student (in writing) how to solve the problem. Be sure to justify your steps."

Differentiated Instruction
MEETS EXPECTATIONS

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The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teachers in differentiating instruction for diverse learners within and across grades. The materials offer lessons that are scaffolded to allow a range of learners to gain entry into the problems. The materials provide multiple language translators so that students of various backgrounds can engage in the mathematics in their native language. Additionally, teachers are offered ideas and suggestions for grouping all learners in a variety of ways.

Criterion 3r-3y

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

2/2
Indicator 3r

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide strategies to help teachers sequence or scaffold lessons so the content is accessible to all learners. A "universal access" guide with directions on scaffolding for ELL and special needs students is provided. One strategy included is to focus on checkpoint or essential problems for struggling learners so that they have access to the same level of rigor but with fewer problems.

2/2
Indicator 3s

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide teachers with strategies meeting the needs of a range of learners. There are eBook materials in the teacher resources that include a list of strategies for a wide range of learners. Specifically, the Universal Access Guidebook and Literacy Guidebook explain how to assist students who are making normal progress, or need additional help, or are underprepared for the course, or who have special needs such as English language learners, advanced learners or struggling readers.

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Indicator 3t

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations. There are many investigations and modeling problems that allow for multiple solutions and strategies. Many problems encourage multiple representations (graph, verbal, analytical, numerical). Most of the beginning lessons within a chapter offer scaffolding that allows multiple entry points into the opening problem, which allows for students with a range of learning abilities to have access to the problem.

  • For example, Algebra 1, lesson 5.1.1, opens the chapter on sequences with an investigation of two friends who dream of raising rabbits. The question gives a scenario and asks how many rabbits would there be after one year. There are four questions that ask students to identify patterns and make predictions, thinking in teams about the strategies they would use. Problem 5-2 is designed for further guidance for students who need more direct strategies to use. These strategies include drawing a diagram, creating a table and looking at specific patterns. Eventually, students will work their way to recursive equations, explicit equations and graphing of these equations and the functions these equations represent.
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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).

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. The series clearly identifies checkpoint problems and core problems with guidance on how to modify the pacing for special populations so all students have access to on grade level resources. "Math Note" sections throughout the lesson provide definitions and examples with regard to vocabulary. Additionally, every lesson is provided in Spanish, and through the eBook translator, can be translated into most languages.

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Indicator 3v

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

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. A pacing guide shows pacing for students who are at grade level as well as those who are advanced. For advanced students most lessons include enrichment and additional problems within the lesson. The teacher materials explicitly state that advanced students also benefit from the richness of the problems in the text and will often be able to develop considerable depth in their work. Examples of enrichment and additional problems include, but are not limited to:

  • In Geometry lesson 6.2.3, the teacher materials note that problem 6-72 is an extension. Problem 6-68 is the core problem, while 6-69 and 6-70 are optional problems needed for further guidance.
  • In Algebra 1 lesson 4.2.2, the teacher materials note the core problems as 4-42 and 4-47. Problems 4-43 through 4-45 are noted as further guidance or enrichment problems.
Indicator 3w

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

The instructional materials reviewed for the High School CPM Traditional series provide a neutral portrayal of various demographic and personal characteristics. The names and situations portrayed in the book are diverse.

Indicator 3x

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

The materials provide opportunities and directions for teachers to use a variety of grouping strategies. The materials focus on team cooperative learning. Additionally, the materials provide activities, discussions, and tasks tailored for whole group, team and individual work. Examples include, but are not limited to:

  • In Algebra 2 lesson 4.1.3, the teacher materials refer to three different grouping strategies to use throughout the lesson. When the user clicks on the strategy, a pop-up box appears that defines the purpose of the strategy and gives a full explanation of how to use the strategy. This full explanation includes materials needed, classroom management tips, the full protocol of how to use the strategy and sometimes links to other resources for more information about the strategy.
  • In Geometry lesson 2.2.3, the teacher materials suggest students work in teams on three different problems. As the students are working in the teams, the teacher has been provided with specific questions to ask while circulating among the teams. The closure activity then involves a cooperative Pairs Check strategy, again that is included with a pop-up box to know how to best execute that strategy in the class. There is also a team strategy part of the lesson that supports the teacher with strategies to help the teams as they are collaborating during the lesson.
Indicator 3y

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

The materials encourage teachers to draw upon home language and culture to facilitate learning. The eBook materials include a translation link for every lesson. All lessons in the eBook have tabs for both English and Spanish.

Effective Technology Use

The instructional materials reviewed for the High School CPM Traditional series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide access to many e-tools through the eBook. Additionally, the materials allow teachers to create their own assessments as well as collaborate with other teachers who are also using the same materials.

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.

The materials integrate technology, manipulatives and dynamic software in ways that engage students in the MPs. The materials have their own collection of virtual manipulatives which includes algebra tiles, base ten blocks, probability tools, data representation tools, transformation tools, similarity toolkit, numbers lines and graphing tools. Additionally, the materials make regular use of pre-made Desmos.com graphs and other pre-made applets. Examples include, but are not limited to:

  • In Algebra 1 lesson 6.1.4, the eBook student materials link directly to four different Desmos.com files that assist with understanding lines of best fit in the problems that are a part of that lesson.
  • In Geometry lesson 3.2.1, the eBook student materials link directly to seven different CPM eTool dynamic applets to work with pre-made or to create your own sketches in thinking about and exploring similar triangles.
  • In Algebra 2 lesson 7.1.3, the eBook student materials link directly to four different Desmos.com files for explorations of reference angles and trigonometric graphs.
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.

The digital materials are web-based and compatible with multiple internet browsers. The series uses Quicktime, YouTube, and internet resources that are accessible on multiple devices and browsers. Quicktime player needs to be installed on computers. HTML5 works on most mobile devices and on many computers. YouTube may not be allowed at all schools.

Indicator 3ab

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

The materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. Teachers have test bank available through the eBook. Assessments are not available for students through the eBook and are not adaptive, but teachers can customize assessments using the test bank.

Indicator 3ac

Materials can be easily customized for individual learners.

Indicator 3ac.i

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

The materials in the series do not provide adaptive technology.

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.

The technology components offered in the materials are not customizable for students based on their needs or interests.

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.).

The materials provide opportunities for teacher to collaborate with each other through the eBook resources via a sharing tab. There are not opportunities for student to student or student to teacher collaboration via the eBook.