CPM Integrated, Exercises of Mathematics

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Alignment: Overall Summary

CPM Integrated

CPM Educational Program (CPM) |

High School

The instructional materials reviewed for the CPM Integrated series meet expectations

for alignment to the CCSSM for high school. The materials meet the expectations for

focus and coherence. The materials attend to the full intent of the mathematical

content standards and 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 reect 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.

SEE RATING SCALE UNDERSTANDING GATEWAYS

Gateway 1: FOCUS & COHERENCE

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

Gateway 2: RIGOR & MATHEMATICAL PRACTICES

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

Gateway 3: USABILITY

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

Gateway One Focus & Coherence

Meets Expectations

 

ALIGNMENT | Meets Expectations

0 9 14 18

0 9 14 16

USABILITY | Meets Expectations

0 21 30 36

CRITERION 1A - 1F

15

16

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The instructional materials reviewed for the High School CPM Integrated series meet the expectation that the materials attend to the full intent of the modeling process when applied to the modeling standards. The series includes modeling tasks throughout the materials. Frequently, tasks include signicant scaolding or support to focus students on specic mathematics, but scaolding of modeling tasks decreases within a course and over the series helping to develop students' abilities to work with modeling tasks. In the series, students have opportunities to develop their own solution strategies, select the best tools for solving a problem or set of problems, create their own charts, graphs, and/or equations, evaluate and revise answers, and report on their work.

In Lesson 2.1.3 of Integrated I, the problem “How Steep Is It?” has students use a model, stairs, to represent the slope of a function. This problem asks students to make, use, and describe a model, but it does not engage them in the full modeling process as dened by the Modeling, High School Progressions Document. This problem addresses standards F-IF.4, F-IF.6, F-IF.7a, F-LE.1a, F-LE. and F-LE.5. In Integrated I, “The Big Race - Finals” problem in Lesson 2.2.3 has students engage in parts of the modeling process, such as dening variables, interpreting data, validating their conclusions, and reporting out to other teams. However, the students do not come to develop the question themselves, and they do not collect the data for the investigation themselves. All of this is explicitly given to them by the materials. This problem addresses standards N-Q.2, A-CED.2, F-IF.4, F- IF.7a, F-BF.1a, F-LE.1b, F-LE.2 and F-LE.5. In “The Burning Candle” problem in Lesson 11.2.3 of Integrated I, students are presented a real-life situation that should be engaging for Integrated I students. The students are asked to design an experiment, collect data and analyze data in order to predict how long a birthday candle will stay lit. The problem appropriately engages students in all aspects of the modeling process. This problem eectively engages students in applying the modeling process to standards N-Q.2, N-Q.3, A- CED.1, F-IF.7a, F-BF.1a, F-LE.2, S-ID.6a, S-ID.6c, S-ID.7 and S-ID. In Integrated II, Lesson 1.2.1 uses a bracelet task to have students perform an experiment and then collect, record and analyze data. Next, they are prompted to modify the experiment, collect, record and analyze new data, and compare the new data set to their rst set of results. Finally, the students are prompted to design their own experiment “spin o” of the original and then collect, record and analyze their data. If the lesson is followed through to the end, every aspect of the modeling process would be completed by the students. Right below this task is a owchart example of modeling with mathematics. In Integrated II, “Standards to Maintain” the “Shrinking Targets Lab” in Lesson 9.1.1 has students dene variables, collect and analyze data and then use their data to extrapolate. They are provided a signicant level of support, but they are still actively engaged in the modeling process. This lab addresses standards A-CED.2, F-IF.4, F-IF.5, F-IF.7a and F-BF.1a. In Integrated III, Lesson 6.1.1 has students use coins to model whether a child is born a girl or a boy. The students design the experiment and then record and analyze their results. They are given many parameters that prevent students from determining their own variables. The students share and compare their data with other teams, and they also compile their data and analyze if/how the data changes when the sample size is larger. This lesson addresses standards S-IC.2 and S-MD.6(+).

In Integrated III, Lesson 6.2.1 has students design a computer simulation to model a real-life situation and then collect and analyze data. This lesson addresses standards S-IC.1, S-IC.4 and S- IC.5. In Integrated III, Lesson 9.1.1 (F-TF.5) introduces a task entitled "Emergency!" The experiment procedure is outlined in the materials. The specic directions provided allow for students to focus on the appropriate mathematics and do not detract from the modeling process. Students are asked guiding questions that require them to develop their own strategies for solving the problem and reect on the dierence between their process and the process of others.

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.

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 materials, when used as designed, 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 show a strong focus on widely applicable prerequisites.

The majority of the lessons in Integrated I focus on the WAPs. Chapters 1, 2, 3, 5, 6, 7, 8, 9 and 11 had lessons in which the majority of the time was spent on the WAPs. There are some lessons that review middle school mathematics standards, but this does not occur in a way that is distracting or in a way that takes time away from the WAPs. For example Section 1.3 is projected to last approximately two days and reviews rewriting expression with integer exponents (8.EE.1). Also, Appendix A provides review activities for rewriting expressions (7.EE.1). These sections provide opportunities to support struggling learners and clear up misconceptions but could easily be omitted if not needed by the students. The majority of the lessons in Integrated II are spent on the WAPs. Chapters 1, 2, 3, 4, 5, 6, 7 and 9 included lessons which were primarily focused on the WAPs. Chapters 8, 10, 11 and 12 are not focused on the WAPs, but their content does t the ow of content through the materials. Section 1 of Chapter 1 spends time reviewing attributes of polygons which aligns to middle school standards. In Integrated III, approximately half of the lessons focus on WAP standards. The progression and ow of the materials are logical and support a deep understanding of the mathematics. Chapters 1, 2, 3, 5 and 7 included lessons in which the majority of the work was related to the WAPs.

Overall, the majority of student time is spent on the widely applicable prerequisites.

INDICATOR 1B.II

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The instructional materials reviewed fully meet the expectations for students to engage in mathematics at a level of sophistication appropriate to high school. The materials give extensive opportunities to work with course-level problems and exercises appropriate to high school and relate new concepts to students' prior skills and knowledge.

The Universal Access section allows all students an opportunity for entry points to the content. There is appropriate guidance for the teacher to help scaold for dierent students, and the level of scaolding and support is appropriate and does not impede students from engaging in the full intent of the mathematics.

Contextual problems are appropriate for high school students. Several contextual problems complement content that students learn in other core classes, such as farming and sustainability, exercise, and genetics.

Scenarios presented in application problems are authentic, as well as adjustable to dierent interests. Examples of authentic application and/or real world problems include the following:

In Integrated I, Lesson 1.1.2 uses three contextual scenarios, placement of tiles in a yard, modeling the spread of a u epidemic, and time it takes to sign your name on multiple documents, in order to teach growth of patterns. In Integrated II, Lesson 3.1.3 uses a rock-paper-scissors game with scoring rules which may or may not be fair. Students have to decide the fairness based on their knowledge of probability models. In Integrated III, Lesson 6.2.1 focuses on statistical testing using sampling variability. The lesson poses a question of whether students support keeping or canceling a winter formal dance. Students work with appropriate numbers for high school and see a wide variety in equation/expression formats.

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

All conceptual categories are addressed over each of the courses. Each course contains work in number and quantity, algebra, functions, geometry, and statistics and probability. Topics are addressed when they are developmentally appropriate. More concrete ideas are examined in Integrated I while more abstract ideas are examined in Integrated III. The progression of diculty is logical.

The following are examples of connections made between the books in the series:

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Connections are made throughout every course in the Review & Preview portion of every Section. These problems connect with prior work in both the current course and past courses (if any), the current topic, and future topics (usually using the preview problems to review skills and concepts for work that is immediately upcoming). In Integrated II, Chapter 2 provides students the opportunity to make connections from their work on congruence in Integrated I with a brief review of congruence theorems to the work that they will do with similarity and dilations. The following are examples of connections made within the books in the series:

In Integrated I, Chapter 7 starts by engaging students in what it means for two gures to be congruent, and then it engages in determining the least amount of information needed for proving two gures to be congruent. It proves triangle congruence criteria using rigid motions. Then it has the opportunity to connect that work to the coordinate plane. The students study polygons on the coordinate grid by proving statements about the gures using coordinate geometry and relationships for distance, slope, and midpoint. In Integrated II Chapter 9, Modeling with Functions, the study of quadratic associations in statistics and probability builds on students' understanding of quadratic relationships, from Chapters 2, 5 and

The materials are designed to spiral concepts throughout the chapters and courses. Some topics included within the same chapter are disconnected. These were placed this way intentionally to allow students more time with the rst concepts in Review & Preview before the concept is developed further in a future chapter.

In Integrated III, Chapter 7 is on logarithms and triangles. The connection between logarithms and triangles is not evident. In Integrated II, Chapter 7 is about Proof and Conditional Probability, and Chapter 3 is about Probability and Trigonometry. The connection between these topics is not evident.

INDICATOR 1E The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The instructional materials reviewed partially meet the expectations that the series explicitly identify and build on knowledge from Grades 6-8 to the High School Standards. The content that is identied as being from previous grades is appropriate and develops as a natural progression into high school, but it is not always clearly connected to a specic middle school standard.

The following are examples of connections made between content from Grades 6-8 and the high school content:

Integrated I:

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In Chapter 6, Lesson 6.1.4 states that students learned about the laws of exponents in a previous course.

INDICATOR 1F The plus (+) standards, when included, are explicitly identied 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 Integrated 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.

In most cases, it would be dicult to separate out the plus standards material from the non-plus standards. However, work with the plus standards does not deter from the work with the non-plus standards. An example of where it could easily be separated is in Integrated II, Chapter 12, which is comprised of primarily plus standards; this section could be omitted. The materials, however, oer no guidance or pacing suggestions should teachers not wish to use the plus standards.

The plus standards that are identied in the teacher resource binder and addressed to reach the full intent of the standard are listed below:

Integrated I does not address any plus standards. Integrated II: N-CN.8 (Lessons 5.2.6 and 6.2.4); N-CN.9 (Lesson 6.2.4); G-C.4 (Lesson 10.2.5); S-CP.8 (Lesson 7.2.3); S-CP.9 (Lessons 12.1.1-12.1.4 and 12.2.4); S-MD.6 (Lessons 3.1.5, 12.1.1- 12.1.3 and 12.2.4); S-MD.7 (Lessons 6.2.6, 7.2.3, 12.1.1, 12.2.1 and 12.2.4) Integrated III: N-CN.8 (Lessons 8.2.2 and 8.3.4); N-CN.9 (Lessons 8.1.1, 8.1.2, 8.2.1, 8.2.2, and 8.3.2); A-APR.5 (Lessons 10.3.1-10.3.3); A-APR.7 (Lessons 11.1-11.1.4 ); F-TF.9 (Lessons 12.2.1, 12.2.2 and 12.2.3); G-SRT.9 (Lessons 7.2.1 and 7.2.2); G-SRT.10 (Lessons 7.2.1-7.2.4); G-SRT. (Lesson 7.2.5); S-MD.6 (Lessons 6.1.1, 6.1.2 and 6.3.1); S-MD.7 (Lesson 6.2.3)

One plus standard is assessed on checkpoints. Standard N-CN.8 is assessed on Integrated III Checkpoint 11.

Gateway Two Rigor & Mathematical Practices

Meets Expectations

CRITERION 2A - 2D Rigor and Balance: The instructional materials reect 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 uency; and engaging applications. 8/

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 specic content standards or clusters.

The instructional materials reviewed for the High School CPM Integrated series meet the expectation that materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specic content standards or clusters. Overall, the clusters and standards that specically relate to conceptual understandings are thoroughly addressed.

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 reections on and synthesis of the connections to what the learning targets were for the chapter.

Some examples of the intentional development of conceptual understanding are as follows.

In Integrated II, Lesson 3.1.1 introduces students to probability area models by analyzing the frequency of inherited traits. This lesson builds on concepts that would be introduced and developed in a middle school science course and relates that knowledge to the new mathematics concept. The materials begin with simple scenarios and guide students to more complex situations to apply area models. Lesson 8.3.1 in Integrated II, which contains the Mighty Mascot problem, provides students with a simple real world example of scale factor to which students can easily visualize and relate. Then, the students are asked to make observations and look for patterns in the relationships between scale factor, area, and perimeter. Finally, the students are asked to apply these observations and patterns to other situations. In Integrated III, Chapter 6, Simulating Sampling Variability, begins with simple probability examples that students should be familiar with (tossing coins, playing cards) to introduce the new concept. Then, the materials expose students to more complicated situations in which to apply the concept. In Integrated III, Lesson 10.1.1 helps students develop the concept of arithmetic sequences and prepares them to determine the sums of arithmetic sequences. To introduce this concept, the materials begin with the real world situation of saving money for college, a topic very appropriate

The instructional materials reviewed for the High School CPM Integrated series meet the expectations for rigor and balance. Overall, all three elements of rigor are thoroughly attended to and interwoven in a way that focuses on addressing specic standards as well as balancing procedural skill and uency, application, and conceptual understanding within individual courses and across the series as a whole.

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Examples of select cluster(s) or standard(s) that specically relate to procedural skill and uency include, but are not limited to:

A-APR.1: Students practice operations on polynomials in many lessons including Integrated II, Lessons 1.2.3, 4.1.3-4.1.4 and 5.2.6, and Integrated III, Lessons 1.1.4 and 8.3.1. F-BF.3: Students use transformations on functions in Integrated I, Lesson 10.2.1, by examining the eect of adding a constant to a function. In Integrated II, Lessons 9.1.2-9.1.4 expand transformations to include dilations and shifts in any direction on parabolas and absolute value functions. Integrated III expands to include additional types of functions. Lessons 2.2.1-2.2. expand to include cubic, rational and root functions and non-functions such as circles. Lesson 5.2. includes logarithmic functions and Lessons 9.2.1-9.2.4 include periodic functions. G-SRT.5: Ample practice is provided in Integrated II, Lessons 2.1.1, 2.1.2 and 2.3.1-2.3.4, in determining similarity/congruence and using these characteristics to nd missing sides and angles.

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 specic content standards or clusters.

The instructional materials reviewed for the High School CPM Integrated 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 specic content standards or clusters.

Students frequently solve non-routine application problems that develop the mathematics of the standards. Students are provided opportunities to make their own assumptions, question, investigate, critically analyze and communicate their thinking in teams, independently and in Learning Logs as they model mathematical situations.

In Integrated I, Lesson 2.2.2 students graph and write equations to describe the real-life situation of runners in a race. The materials use the context to provide opportunities for students to apply contextual meaning to interpret parts of an expression in terms of its context. (A-SSE.1b) In Integrated II, Lesson 5.1.2 students apply what they have learned about quadratic functions to the context of a water balloon contest. The students relate the intercepts and vertex of a parabola to the launch, landing, and maximum height of a launched water balloon. (F-IF.4) In Integrated III, Lesson 4.1.2 students compare the representative nature of samples selected using intentional choice with those selected randomly by applying this concept in a real-life scenario involving astronomers determining the average diameter of asteroids captured by a satellite image. (S-IC.1)

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.

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The instructional materials reviewed for the High School CPM Integrated 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 that all three aspects of rigor are 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.

The materials contain a balance of opportunities for students to develop uency in new mathematics concepts and to apply these skills in engaging tasks. The materials consistently present students with problems that include real world application and signicance whenever appropriate. As needed, students are provided opportunities to practice skills for procedural uency. This balance is maintained throughout the course. The balance of procedural skill development and application is not rigid throughout the materials and changes based on the targeted concept.

In Integrated I, Chapter 1, Lesson 1.1.1 builds conceptual understanding and uency by having students work in teams to evaluate expressions, build “function machines” to connect inputs and outputs, and make observations and generalizations about functions. Lesson 1.1.2 has students work in collaborative teams to complete labs where they collect and analyze data. In Integrated I, Chapter 6, Lessons 6.1.1 and 6.1.2 focus on procedural skills such as rearranging linear equations to y = mx+b form, solving equations, and nding the missing terms in a sequence. Then, in 6.1.3, students engage in tasks that apply these skills in real world context. In Section 3.1 of Integrated II, every lesson provides context and application for the skills the students are exploring. The materials did not decontextualize to teach the probability models. The materials address the concepts within real world examples and scaold students to a level of deep conceptual understanding. In Lesson 3.2.1, students are introduced to a new concept (constant ratios in right triangles) within a rich context, and then in Lesson 3.2.2, the materials have students practice the procedural skill and build uency for connecting slope ratios to specic angles. In Chapter 1 of Integrated III, Investigations and Functions, the lessons in Section 1 focus mainly on procedural uency with functions, and Section 2 focuses on application in a rich context. In Chapter 4 of Integrated III, Natural Distributions and Geometric Modeling, the lessons include many real world application problems and fewer procedural uency problems as is appropriate for the concept.

CRITERION 2E - 2H Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for the High School CPM Integrated series meet the expectation that materials support the intentional development of all eight MPs, in connection to the high school content standards. The teacher resources for each course includes a "Correlation of CPM Core

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The instructional materials reviewed for the High School CPM Integrated 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 inherently found in the text, and these practices are not treated as isolated experiences for the students. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others.

Some examples of MP2 and MP3 are as follows:

In Integrated I, Lesson 2.3.1 has students decontextualize and examine the situation numerically, and they recontextualize by examining the numbers in terms of the original problem situation. In Lesson 10.1.2 of Integrated I, students must make choices about data displays and defend their choices. In Integrated II, Lesson 3.2.4 connects the tangent ratio to the slope of a line. In Integrated II, Lesson 7.2.3 has students construct arguments as they explain their thinking about independent situations. In Lesson 3.2.4 of Integrated III, students construct viable arguments and critique the reasoning of others about a hypothetical mathematics contest. In Integrated III, Lesson 4.4.3 introduces a 3-D printing design problem, and students must reason about the quantities and what they represent. They must also formulate a rationale for their choices.

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 Integrated 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 MPs. Overall, the majority of the time MP4 and MP5 are used to enrich the mathematical content inherently found in the text, and these practices are not treated as isolated experiences for the students. Throughout the materials, students are expected to model with mathematics and use tools strategically.

Some examples of MP4 and MP5 are as follows:

In Integrated I, Lesson 1.1.2 has students determine an organized way to record their data. In Lesson 6.4.1 of Integrated I, students decide which strategy is most ecient when solving systems of equations. In Integrated I, Lesson 10.1.2 models a golf game by tossing pennies and measuring the distance from a hole. Students collect data using this model and must make decisions about the tools involved in measurement, data collection, and data display.

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In Integrated II, Lesson 6.2.1 has students model a tennis serve. In Lesson 10.2.5 of Integrated II, students model orbiting satellites and perform constructions. In Integrated III, Lesson 7.2.1 presents problems with missing parts of triangles. Students determine the information necessary to nd the missing measurements. Students may need to try multiple solution paths before nding one which will be successful, and they also need to consider multiple cases and combinations of known and unknown parts in both right and non-right triangles.

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 Integrated 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 MPs. Overall, the majority of the time MP7 and MP8 are used to enrich the mathematical content inherently found in the text, and these practices are not treated as isolated experiences for the students. Throughout the materials, students are expected to see structure and generalize.

Some examples of MP7 and MP8 are as follows:

In Integrated I, Lesson 3.1.6 has students summarize and generalize the symmetry of gures. In Integrated I, Lesson 5.3.1 examines growth rates. In Lesson 4.1.3 of Integrated II, students attend to aspects of MP7 and MP8 while factoring general and special quadratics. In Integrated II, Lesson 8.2.1 has students "use repeated reasoning to generalize a process for determining the sum of the interior angles of a polygon and then make use of structure to calculate individual interior and exterior angle measures in regular polygons." In Integrated III, Lessons 2.2.1 and 2.2.4 examine the structure of equations in conjunction with repeated reasoning to make sense of transformations of both functions and non-function equations. In Lesson 2.2.1, students "look for and make use of structure and look for and express regularity in repeated reasoning as they make connections between the transformations of parabolas and the transformations of other parent graphs." In Lesson 8.3.4 of Integrated III, students consider factoring patterns for special polynomials and compare dierences of powers as special cases of dierences of squares.

Gateway Three Usability

Meets Expectations

CRITERION 3A - 3E

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The instructional materials reviewed for the High School CPM Integrated series meet the expectation that students are asked to produce a variety of products during the lessons in each chapter to demonstrate their learning.

Throughout various lessons and within the problem sets, students are asked to produce answers and solutions as well as to describe their answers, discuss ideas, make conjectures, explain their work and reasoning, make sketches and diagrams, justify their reasoning, and use appropriate models. Students are asked to show work including checking of solutions, drawing visual representations, explaining steps and reasoning and justifying responses.

For example, in Integrated II Lesson 5.1.3, students investigate the minimum number of points to sketch a parabola. Students examine x- and y- intercepts of parabolas and relate these to the equations, make sense of the zero product property, and complete a Learning Log entry. Students also sketch a graph of a quadratic equation. Also, in Integrated II Lesson 6.2.3, students investigate shortest distance problems using physical models and diagrams. Students decide whether answers make sense and explain their rationale.

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 series makes use of a wide range of virtual manipulatives. The materials have their own collection of virtual manipulatives including algebra tiles, probability tools, data representation tools, transformation tools, similarity toolkit, number lines and graphing tools. The materials also make regular use of pre- made 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 specic manipulatives and tools that will be needed for specic lessons. A few examples of these include, but are not limited to: linguini, coee straws, and pennies. Overall, students are exposed to a number of manipulatives and virtual tools and expected to use these as necessary.

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 Integrated series have a visual design that is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The layout of both the online text and the print materials is not distracting. The layout is the same for every lesson and every course. The design of the teacher materials is consistent across lessons and courses. Materials are presented in a manner which aligns to the student textbook.

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The online materials are contained in the largest box on the screen. A small frame on the left side of the screen allows the user to navigate quickly to any section within the textbook and contains links to the index, glossary and other reference materials. Across the top of the window is a tab that allows student to toggle between the Spanish and English translations of the lesson. Below the textbook are links to an online dictionary and translation tools and the online mathematics tools (algebra tiles, probability tools, Desmos, data analysis tools, and transformation tools). These open in a new browser tab. Illustrations in the online textbook are minimal and appear to the right of the problems. They do not distract from the textbook itself.

INDICATOR 3F Materials support teachers in planning and providing eective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials reviewed for the High School CPM Integrated series meet the expectation that the materials support teachers in planning and providing eective learning experiences by providing quality questions to help guide students' mathematical development.

Guiding questions are provided in the teacher materials. These are usually found in the "Suggested Lesson Activity" section, although sometimes can be found in the "Universal Access" or "Team Strategies" sections. For example, in Integrated III Lesson 8.1.1, teacher materials focus on questions connecting the number of roots of a polynomial with the degree of the polynomial. Example questions include the following: “What if you multiply by another factor?” “How will multiplying by another factor aect the graph?” “How will it aect the equation?” “What might the graph look like if the highest power of x were ve or six?”.

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.

CRITERION 3F - 3L Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for the High School CPM Integrated 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, the student with guiding questions for appropriate mathematical development and the parents with resources.

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