Mathematics Idaho Core Standards€¦ · · 2017-12-20measurement data, scatter plots, trend line, line of best fit, correlation. ... the unit rate as the slope of the graph and

Publisher: __ Pearson Education, Inc.__________________________ Title of Material: Pearson Connected Mathematics 3, Grade 8 Algebra 1_ Author: Lappan et al. __ ISBN #: _9780133296778_____________________ Copyright__2014__ Reviewers: ______________________________________________ Meets Content Standards Alignment: _______Yes _______ No Meets Literacy Standards Alignment: _______Yes _______ No Meets Material Analysis Evaluation: _______Yes _______ No _____ Recommended as a: (See notes at the end of the evaluation.) _____ Core Program _____ Component Program _____ Intervention Program _____ Supplemental/Resource _____ NOT Recommended – Please explain __________________________________ _________________________________________________________________________ (See additional notes page at end of the evaluation.)

Mathematics Idaho Core Standards

Grades 6-8

Criterion- Adapted from Instructional Materials Evaluation Toolkit (IMET)

Evidence- Publisher/Provider: List units with specific examples of where standards are Introduced/Taught/Assessed.

Include a narrative explanation. Be specific. (Reviewer: Add notes.)

Rating: (Reviewer)

Non-Negotiable 1: Freedom from Obstacles to Focus Materials must reflect the content architecture of the Standards by not assessing the topics named before the grade level where they first appear in the Standards.

Required Materials • Common Core State Standards for Mathematics (www.corestandards.org/wp-content/uploads/Math_Standards.pdf) • Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013) (http://www. corestandards.org/wp-content/uploads/Math_Publishers_ Criteria_K-8_Spring_2013_FINAL1.pdf) • From the materials being evaluated: teacher guides and all assessment components

Rating this Criterion: Non-Negotiable 1 is rated as Meets or Does Not Meet. To rate Non-Negotiable 1, begin by rating Metric 1A. Since Metric 1A is the only metric for Non-Negotiable 1, the rating for Non-Negotiable 1 is the same as the rating for Metric 1A. If Metric 1A is rated as Does Not Meet, include evidence of when the named topic(s) is/are assessed. If the metric is rated as Meets, list the grade(s) examined in the evaluation.




Rating: (Reviewer)

Metric NN1A: Materials reflect the basic architecture of the Standards by not assessing the listed topics before the grade level indicated. • Probability, including chance, likely outcomes, probability models. (Introduced in the CCSSM in grade 7) • Statistical distributions, including center, variation, clumping, outliers, mean, median, mode, range, quartiles; and statistical association or trends, including two-way tables, bivariate measurement data, scatter plots, trend line, line of best fit, correlation. (Introduced in the CCSSM in grade 6) • Similarity, congruence, or geometric transformations. (Introduced in the CCSSM in grade 8) • Symmetry of shapes, including line/ reflection symmetry, rotational symmetry. (Introduced in the CCSSM in grade 4) How to Find the Evidence: Evaluate the table of contents, all chapter tests, all unit tests, and other such assessment components (including rubrics). For context, read Criterion #2 from the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013). NOTE: Grade alignments of other topics are addressed in Non- Negotiable 2, Focus and Coherence.)

Evidence- Probability, including chance, likely outcomes, and probability models, is introduced in Connected Mathematics 3 in Grade 7: Samples and Populations. Statistical distributions, including center, variation, clumping, outliers, mean, median, mode, range, quartiles; and statistical association or trends, including two-way tables, bivariate measurement data, scatter plots, trend line, line of best fit, and correlation are introduced in Connected Mathematics 3 in Grade 6: Data About Us. Similarity is introduced in Connected Mathematics 3 in Grade 7: Stretching and Shrinking. Congruence and geometric transformations are introduced in Connected Mathematics 3 Grade 8: Butterflies, Pinwheels, and Wallpaper. Students’ familiarity with symmetry and their understanding of related concepts are assumed and applied in Connected Mathematics 3 in Grade 6: Covering and Surrounding; Grade 7: Shapes and Designs, Stretching and Shrinking, Filling and Wrapping; and Grade 8: Butterflies, Pinwheels, and Wallpaper.

____Meets ____Does Not Meet

NN 1 Rating ____Meets ____Does Not Meet

Comments: (Be Specific)




Rating: (Reviewer)

Strengths: Weaknesses:




Rating: (Reviewer)

Non-Negotiable 2: Focus and Coherence Materials must focus coherently on the Major Work of the grade in a way that is consistent with the progressions in the Standards.

Required Materials • Common Core State Standards for Mathematics (http:// corestandards.org/wp-content/uploads/Math_Standards.pdf) • Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013) (http://www. corestandards.org/wp-content/uploads/Math_Publishers_

Criteria_K-8_Spring_2013_FINAL1.pdf) • Focus by Grade Level for the grade being evaluated (www. achievethecore.org/focus) • From the materials being evaluated: teacher guides, student

texts and workbooks

Rating this Criterion: Non-Negotiable 2 is rated as Meets or Does Not Meet. To rate Non-Negotiable 2, first rate metrics 2A–2H. Each of these eight metrics must be rated as Meets in order for Non-Negotiable 2 to be rated as Meets. Rate each metric 2A-2H as Meets or Does Not Meet/Insufficient Evidence. If the evidence examined shows that the Criterion is met, then mark the Criterion Meets. If the evidence examined shows that the Criterion is not met—or if there is insufficient evidence to make a determination—then mark the Criterion as Does Not Meet/Insufficient Evidence. Support all ratings with evidence.




Rating: (Reviewer)

Metric NN2A: In each grade K–8, students and teachers using the materials as designed devote the large majority of time to the Major Work of the grade. How to Find the Evidence: Familiarize yourself with the Major Work of the grade being evaluated (see the Focus by Grade Level documents.) Evaluate the table of contents and any pacing guides. Do not stop there; also evaluate units, chapters, lessons, homework assignments, and assessments. (Evaluate both student and teacher materials.) Consider time spent on the Major Work of the grade and judge qualitatively whether students and teachers using the materials as designed will devote the large majority of time to the Major Work of the grade. For context, read Criterion #1 in the Publishers’ Criteria for the Common Core State Standards for Mathematics,

Evidence-

The table indicates the days and percent of class time spent in Connected Mathematics 3 in the Major Clusters of Expressions and Equations (work with radicals and integer exponents; understand the connections between proportional relationships, lines, and linear equations; analyze and solve linear equations and pairs of simultaneous linear equations), Functions (define, evaluate, and compare functions), and Geometry (understand congruence and similarity using physical models, transparencies, or geometry software; understand the Pythagorean Theorem). 113 days, or 71% of total class time, is devoted to studying concepts in these areas. In terms of covering the Major Work of the Algebra CCSS, the only Additional Content being taught in CMP3 Algebra is solving systems of equations (It’s in the System). Otherwise, all of the Major Clusters of Algebra are covered by the CMP3 Grade 8/Algebra 1 series. The Major Work added with the Algebra standards includes the following:

Interpret the structure of expressions Perform arithmetic operations on polynomials Create equations that describe numbers or relationships Understand solving equations as a process of reasoning and explain the

reasoning Solve equations and inequalities in one variable Represent and solve equations and inequalities graphically Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context

____Meets ____Does Not Meet/ Insufficient Evidence




Rating: (Reviewer)

Metric NN2B: Supporting Work, where present, enhances focus and coherence simultaneously by also engaging students in the Major Work of the grade. How to Find the Evidence: Familiarize yourself with the Major Work and Supporting Work of the grade being evaluated (see the Focus by Grade Level documents.) Evaluate chapters and lessons that focus on Supporting Work. NOTE: Example of evaluating this Criterion might include looking at whether materials for K–5 generally treat data displays as an occasion for solving grade-level word problems using the four operations (e.g., see 3.MD.B.3); or whether materials for grade 7 take advantage of opportunities to use probability to support ratios, proportions, and percentages. For context, read Criterion #3 in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- While studying statistics and probability concepts, or Supporting Work, in Grade 8 Connected Mathematics 3, students are actually engaging in the Major Work of the grade. For example, in the Grade 8 CMP3 Unit Thinking with Mathematical Models, students explore the concepts of data patterns and variability and association in numeric and categorical data. While investigating these concepts, students are also doing Major Work in the clusters of Functions and Expressions and Equations: compare properties of two functions each represented in a different way (8.F.A.2); interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear (8.F.A.3); construct a function to model a linear relationship between two quantities (8.F.B.4); describe qualitatively the functional relationship between two quantities by analyzing a graph (8.F.B.5); graph proportional relationships, interpreting the unit rate as the slope of the graph and compare two different proportional relationships represented in different ways (8.EE.B.5); solve linear equations in one variable (8.EE.C.7); and analyze and solve pairs of simultaneous linear equations (8.EE.C.8). With regard to Algebra content, the activities which constitute Supporting Content are reason quantitatively and use units to solve problems; write expressions in equivalent forms to solve problems; and understand the relationship between zeros and factors. All of these standards do support the Major Clusters of Algebra as listed above.





Rating: (Reviewer)

Metric NN2C: Materials base content progressions on the grade-by-grade progressions in the Standards. Content from previous or future grades does not unduly interfere with or displace on-grade-level content. How to Find the Evidence: Evaluate the table of contents and any pacing guides. Do not stop there; also evaluate units, chapters, and lessons in both student and teacher materials. NOTE: In some cases it may be possible that aligned materials might address some aspects of a topic in a strategic way before or after the grade level in which the topic is central in the Standards’ progressions; for example, a curriculum author might purposefully choose to explore adding fractions with unlike denominators in a way appropriate to grade four, recognizing that this work is not really required until the next grade. However, any such purposeful discrepancies in content progressions should enhance the required learning in each grade; not unduly interfere with or displace grade-level content; and be clearly aimed at helping students meet the Standards as written rather than effectively rewriting the progressions in the Standards. And in all cases, note that Non-Negotiable 1 must be met for materials to be aligned. For context, read Criterion #5a in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- The scope and sequence of topics covered in Connected Mathematics 3 are sufficiently distinct between grade levels so as not to interfere with or displace on-grade-level content but at the same time support the progressive content in each of Grades 6 through 8 and Algebra. The topics in Grade 8 proceed from linear and inverse variation (Thinking with Mathematical Models), to the Pythagorean Theorem (Looking for Pythagoras), to exponential functions (Growing, Growing, Growing), to symmetry and transformations (Butterflies, Pinwheels, and Wallpaper), to making sense of symbols (Say It with Symbols), to systems of linear equations and inequalities (It’s in the System). Two topics added for Algebra 1 are quadratic functions (Frogs, Fleas, and Painted Cubes) and families of functions (Function Junction). These topics bridge the gap from concepts and skills learned in 7th Grade to build algebra skills and conceptual understanding, to completely cover the 8th Grade Common Core Standards, and to introduce all of the Algebra Common Core Standards, as well. For example, Grade 8/Algebra 1 students explore linear and exponential functions, and then expand that experience to include other families of functions (Function Junction), including quadratic functions (Frogs, Fleas, and Painted Cubes). One of the Major Clusters in Grade 8 is Functions. The component standards of this cluster are met through student work in the following CMP3 units: Thinking with Mathematical Models (Investigations 1, 2, 3); Growing, Growing, Growing (Investigations 1, 2, 3, 4); and Say It with Symbols (Investigations 1, 2, 3, 4). This cluster continues to be a focus of Major Work in Algebra, with more comprehensive standards. The Algebra CMP3 units which guide students through proficiency and mastery of these standards are Frogs, Fleas, and Painted Cubes: Quadratic Functions and Function Junction: The Families of Functions.





Rating: (Reviewer)

Metric NN2D: Materials give all students extensive work with on-grade-level problems. How to Find the Evidence: Evaluate both student and teacher materials. If the materials provide resources for differentiated learning, consider whether lower-performing students have opportunities to engage with grade-level problems. Also consider whether higher-performing students are given opportunities to learn current grade-level content in greater depth. For context, read Criterion #5b in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- The Connected Mathematics 3 component materials effectively cover the Common Core Standards for mathematics for Grades 6 through 8 and Algebra, and at the same time provide a variety of resources to enable all learners to achieve mastery of these skills and concepts. Embedded strategies, including the availability of technology and manipulatives, support the learning of students with special needs. Real-life problems create meaningful connections for students and improve motivation, participation, and generalization. Repetition and review, especially in the ACE section at the end of every investigation and in the feature, Looking Back, facilitate deeper understanding by unifying mathematical content. Cooperative Learning Groups provide opportunities for all students to participate and succeed. The needs of students who have been identified as gifted or who require advanced work are served by problems which vary in complexity and the organization of content around concepts and abstract ideas. Problems promote higher levels of thinking by emphasizing use over acquisition of information. Open-ended questions stimulate divergent thinking and provide students with opportunities to express their reasoning. Extensions in the ACE assignments often explore beyond what was directly covered in the classroom. In the teacher support materials, there are questions in the Launch-Explore-Summarize features that are labeled, “Going Further.” These questions would be appropriately posed to students who are able to advance beyond the basic curriculum. English Language Learners are served by creating a friendly, supportive, and predictable classroom community; employing modeling and other means of communicating mathematical ideas; and fostering active participation with effective questioning and working in cooperative groups.





Rating: (Reviewer)

Metric NN2E: Materials relate on-grade-level concepts explicitly to prior knowledge from earlier grades. How to Find the Evidence: Evaluate both student and teacher materials. NOTE: Examples of evaluating this Criterion might include looking at the way the materials extend basic ideas of place value across the decimal point; or the role that properties of operations play when the materials extend arithmetic beyond whole numbers to fractions, variables, and expressions. More generally, cluster headings in the Standards sometimes signal key moments where reorganizing and extending previous knowledge is important in order to accommodate new knowledge (e.g., see cluster headings that use the phrase “Apply and extend previous understanding”). For context, read Criterion #5c in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- The term “Connected” in the title, Connected Mathematics 3, refers to a connection of mathematics to the real world; to the unification of investigations, units, and content clusters within and between grade levels; and to the development of goals related to the Common Core standards that span units and grade levels. For example, ratios and proportional reasoning are effectively introduced in Grade 6 and then extended in Grade 7 to the analysis of graphs and symbolic representations of proportional relationships as well as the strategies for solving multi-step ratio and percent problems. Then, in Grade 8, students apply proportions to solve problems involving comparisons of proportional relationships and linear functions and triangle similarity. The number system is expanded from fractions and decimals in Grade 6 to integers in Grade 7 and irrational numbers in Grade 8. The next set of numbers to expand the number system is the set of imaginary and non-real complex numbers. These numbers are referenced in the CCSS in the domain of High School: Number and Quantity.


Metric NN2F: Review of material from previous grades is clearly identified as such to the teacher, and teacher and students can see what their specific responsibility is for the current year. How to Find the Evidence: Evaluate the table of contents, but do not stop there; also evaluate units, chapters, lessons, homework assignments and assessments. (Evaluate both student and teacher materials.) Identify any content from previous grades and check whether it is identified as such. For context, read Criterion #5a in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- In the teacher resources for Connected Mathematics 3, lesson presentation notes are organized within the framework, “Launch-Explore-Summarize.” The Launch section includes information Connecting the current lesson to Prior Knowledge and providing suggestions for reviewing previously learned skills which will be required in the current lesson. Both the teacher materials and the student textbooks clearly indicate the CCSS and goals for each unit, so that students and teachers know what they are supposed to be learning/teaching in a particular unit or investigation. Looking Ahead is a feature at the beginning of each unit in the student textbook that previews each unit and describes its connection to prior knowledge. A recurrent message throughout the program is the understanding that students will be asked to apply anything and everything they have learned to solve new problems on a daily basis.





Rating: (Reviewer)

Metric NN2G: Materials include learning objectives that are visibly shaped by CCSSM cluster headings. How to Find the Evidence: Select several clusters from the Major Work in the grade being evaluated. Evaluate teacher and student materials in relation to these clusters. For context, read Criterion #6a in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Relevant Common Core standards are listed in the student textbook at the beginning of each investigation within each unit of Connected Mathematics 3. The teacher resources also include correlations to standards within each investigation. Mathematical Reflections appear in the student textbook at the conclusion of each investigation. This feature includes open-ended questions requiring students to reflect on what they have learned in the course of the investigation. One or more questions are explicitly related to a Common Core Mathematical Practice. Students are reminded about what practices they have employed, and where, in the course of the current investigation, and they are asked to identify other Mathematical Practices in a sample of a student’s reasoning, and then to describe a Mathematical Practice that they used to solve a different problem within the current investigation.


Metric NN2H: Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. How to Find the Evidence: In the grade being evaluated, choose two or more clusters or two or more domains for which connections are natural and important. Evaluate the units, chapters, and lessons that deal with the chosen topics, looking for problems and activities that serve to connect the chosen clusters or domains. NOTE: An example of evaluating this Criterion might include looking at whether problems in grade 4 sometimes or often involve students applying their developing computation skills (detailed in domain NBT) in the context of solving word problems (detailed in domain OA). For context, read Criterion #6b in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- In Algebra and Grade 8, the CCSS domains explicitly connect at least two content strands, e.g., Expressions and Equations, and Statistics and Probability. The High School Algebra domains include Arithmetic with Polynomials and Rational Expressions and Reasoning with Equations and Inequalities. The teacher materials for Connected Mathematics 3 clearly state that content goals are developed in different ways throughout the course, sometimes in sequence, sometimes in parallel. In Grade 8/Algebra 1, for example, the standards associated with Expressions and Equations are applied in units on mathematical modeling, functions, and geometry. Sample reference: Looking for Pythagoras, Investigation 5, Problem 5.3, page 87


NN 2 Rating ____Meets ____Does Not Meet




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Rating: (Reviewer)

Alignment Criterion 1: Rigor and Balance Materials must reflect the balances in the Standards and help students meet the Standards’ rigorous expectations.

Required Materials • Common Core State Standards for Mathematics (http:// corestandards.org/wp-content/uploads/Math_Standards.pdf) • Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013) (http://www. corestandards.org/wp-content/uploads/Math_Publishers_ Criteria_K-8_Spring_2013_FINAL1.pdf) • Focus by Grade Level for the grade being evaluated (achievethecore.org/focus) • Situation Types for the Operations in Word Problems (achievethecore.org/situation-types) • From the materials being evaluated: teacher guides, student texts and workbooks

Rating this Criterion: Alignment Criterion 1 is rated as Meets or Does Not Meet. To rate Alignment Criterion 1, first rate metrics 1A, 1B, and 1C. Rate each metric as Meets (2 points), Partially Meets (1 point), or Does Not Meet (0 points). For each metric, guiding questions are provided to aid in gathering evidence. Since there are three metrics, and each metric is worth up to 2 points, the maximum possible rating across all three metrics is 6 points. Ideally, aligned materials will earn all 6 points; materials are judged to have met Alignment Criterion 1 if the materials rate 5 or 6 points. This threshold recognizes that evaluators sometimes differ in how they assess features such as rigor and balance, while at the same time ensuring that no single metric can receive a rating of zero and be aligned to the Shifts and major features of the CCSSM.




Rating: (Reviewer)

Metric AC1A: The materials support the development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content Standards or cluster headings.

How to Find the Evidence: Select one or more cluster(s) or Standard(s) from the Major Work for the grade being evaluated that relate specifically conceptual understanding to use throughout the questions associated with this metric. NOTE: Some examples of clusters or Standards that call for conceptual understanding include: K.OA.A.1, (1.NBT.B, 1.NBT.C), (2.NBT.A, 2.NBT.B), (3.OA.A.1, 3.OA.A.2), 4.NF.A, (4.NBT.A, 4.NBT.B), 5.NF.B, (5.NBT.A, 5.NBT.B), 6.RP.A, 6.EE.A.3, 7.NS.A, 7.EE.A, 8.EE.B, 8.F.A, 8.G.A Clusters or Standards grouped by parentheses are closely connected and could be analyzed together. For context, read Criterion #4a in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Is conceptual understanding attended to thoroughly where the Standards set explicit expectations for understanding or interpreting? Do the materials feature high-quality conceptual problems and conceptual discussion questions? Do the materials feature opportunities to identify correspondences across mathematical representations?

____Meets ____Partially Meets ____Does Not Meet




Rating: (Reviewer)

Is conceptual understanding attended to thoroughly where the Standards set explicit expectations for understanding or interpreting? Evaluate lessons, chapter/unit assessments and homework assignments, paying attention to work aligned to Standards that explicitly call for understanding or interpreting. NOTE: Examples of evaluating this Criterion might include looking at how well the multi-digit addition and subtraction algorithms are developed and explained on the basis of place value and properties of operations; or how well the multi-digit multiplication and division algorithms are developed and explained on the basis of place value and properties of operations; or how well solving equations is presented and explained as a process of reasoning.

Evidence- Connected Mathematics 3 emphasizes conceptual understanding through its three-part instructional approach. In the Launch phase, teachers present the problem to the class, which they position within students’ prior learning. Teachers work with students to clarify the task presented in the problem. In the Explore phase, students work together to solve the problem presented, and plan for the presentation of their solution. The Summarize phase consists of students engaging in a discourse about the solutions they have shared. The following table includes Major Cluster CCSS for Grade 8/Algebra 1 which explicitly mandate student understanding correlated to the CMP3 units and investigations where these concepts are introduced and developed.

Standards CMP3 Units and Investigations 8.NS.A.1 Understand informally that every number has a decimal expansion….

Looking for Pythagoras (Investigations 2, 4)

8.EE.C.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs….

It’s in the System (Investigations 1, 2, 3, 4)

8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output.

Thinking with Mathematical Models (Investigations 1, 2, 3)

8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations…. Butterflies, Pinwheels, and

Wallpaper (Investigations 1, 2, 3, 4) 8.G.A.4 Understand that a two-dimensional figure

is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations…. A-APR.A.1 Understand that polynomials form a system analogous to the integers….

Frogs, Fleas, and Painted Cubes (Investigation 2) Function Junction (Investigation 5)





Rating: (Reviewer)

Do the materials feature high-quality conceptual problems and conceptual discussion questions? Evaluate lessons, chapter/unit assessments, and homework assignments. NOTE: Example of conceptual problems might include such questions as “Find a number greater than 1/5 and less than 1/4,” or “If the divisor does not change and the dividend increases, what happens to the quotient?”

Evidence- Within each Connected Mathematics 3 unit, each investigation poses a larger problem to be solved through the concepts and strategies developed throughout the investigation. Smaller problems are posed during the course of the investigation. All of these questions are high-quality, conceptual problems and conceptual discussion questions. At the conclusion of each investigation, ACE assignments include Applications-Connections-Extensions: problems which require an increasing depth of understanding to solve. For example, in Growing, Growing, Growing, Investigation 3, the following problems are posed to students in the ACE assignment: Applications Suppose the price of an item increases 25% per year. What is the growth factor for the price from year to year? Connections Christopher made a drawing so that it measures 8 x 11 inches. He needs to reduce it

so it will fit in a space that measures 7 x 10 inches. What scale factor should he use to get a similar drawing that is small enough to fit? Extensions In Russia, shortly after the breakup of the Soviet Union, the yearly growth factor for inflation was 26. What growth rate (percent increase) is associated with this growth factor? We call this percent increase the inflation rate. (Growing, Growing, Growing, Investigation 3, ACE problems 16, 38, 40)





Rating: (Reviewer)

Do the materials feature opportunities to identify correspondences across mathematical representations? Evaluate lessons, chapter/unit assessments and homework assignments. NOTE: Examples of evaluating this Criterion might include looking at whether students are supported in identifying correspondences among: the verbal description of a situation, the diagrams that distill its mathematical features, and the equations that model it; or equivalent forms of numbers (e.g., 3 and 6/2) and the number line; or rational number operations and representations of them via models such as the vector model; or the expression that defines a function and the graph that shows the relationship.

Evidence- One of the connections featured in Connected Mathematics 3 is the correspondence between different representations of the same concept. In Thinking with Mathematical Models, students explore different ways to use mathematics to represent problem situations. In Say It with Symbols students use variables to represent unknown quantities and to write equations that describe some problem situations. Students model and apply quadratic functions to real-world problems in Frogs and Fleas and Painted Cubes and in Function Junction. Mathematical modeling is an important instructional and learning tool employed throughout CMP3.


Metric AC1B: The materials are designed so that students attain the fluencies and procedural skills required by the Standards. How to Find the Evidence: Select one or more cluster(s) or Standard(s) from the Major Work for the grade being evaluated that relate specifically to fluency and procedural skill to use throughout the questions associated with this metric. NOTE: Some examples of Standards that call for procedural skill and fluency include: K.OA.A.5, 1.OA.C.6, 2.OA.B.2, 2.NBT.B.5, 3.OA.C.7, 3.NBT.A.2, 4.NBT.B.4, 5.NBT.B.5, 6.NS.B.2, and 6.NS.B.3, 6.EE.A, 7.NS.A, 7.EE.A.1,7.EE.B.4a, 8.EE.C.7, 8.EE.C.8b For context, read Criterion #4b in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Is progress toward fluency and procedural skill interwoven with students’ developing conceptual understanding of the operations in question? Are purely procedural problems and exercises present that include cases in which opportunistic strategies are valuable and generic cases that require efficient algorithms present? Do the materials in grades K–6 provide repeated practice toward attainment of fluency Standards?


Is progress toward fluency and procedural skill interwoven with students’ developing conceptual understanding of the operations in question? Evaluate lessons, chapter/unit assessments, daily routines, and homework assignments for evidence that the development of fluency and procedural skill is supported by conceptual understanding.

Evidence- The nature of the problems posed in the instructional pages and the ACE assignments in CMP3 requires students to practice and apply concepts and skills learned in both previous and current units and grades, allowing for frequent opportunities to develop procedural fluency. In Grade 8/Algebra 1, students would benefit from developing fluency with formulas, including the Pythagorean Theorem and other geometry measurement formulas; equations of circles, linear functions, quadratic functions, and exponential functions; and operations that result in various geometric transformations of function graphs.





Rating: (Reviewer)

Are purely procedural problems and exercises present that include cases in which opportunistic strategies are valuable and generic cases that require efficient algorithms present? Evaluate lessons, chapter/unit assessments, daily routines, and homework assignments. NOTE: Examples of problems in which opportunistic strategies are valuable might include the sum 698 + 240 or the system x + y = 1, 2x + 2y = 3. Examples of generic cases that require efficient algorithms might include the sum 8767+2286 or the system 6y + x = x + 3, – x = 1 + 2y.

Evidence- In Grade 8/Algebra 1, students learn to represent rational numbers as terminating or repeating decimals, and to write terminating or repeating decimals as fractions. There is an algorithm which students can use to effectively write a repeating decimal as a fraction, but there are also some patterns which students can use to immediately “see” the fraction represented by any particular repeating decimal. Sample reference: Looking for Pythagoras, Investigation 4, ACE #12-18


Do the materials in grades K–6 provide repeated practice toward attainment of fluency Standards? Evaluate lessons, daily routines, and homework assignments for evidence of repeated practice toward attainment of the following K–6 Standards that set an explicit expectation of fluent (accurate and reasonably fast) computation: K.OA.A.5, 1.OA.C.6, 2.OA.B.2, 2.NBT.B.5, 3.OA.C.7, 3.NBT.A.2, 4.NBT.B.4, 5.NBT.B.5, 6.NS.B.2, 6.NS.B.3.

Evidence- Connected Mathematics 3 provides repeated practice toward the maintenance of computational fluency. For example, in Looking for Pythagoras students explore sums of square numbers and sets of numbers which can be the lengths of sides of a right triangle (and satisfy the Pythagorean Theorem), simplify expressions involving radicals and write equivalent fractions and decimals, including both terminating and also repeating decimals. Sample reference: Looking for Pythagoras, Investigation 3


Metric AC1C: The materials are designed so that teachers and students spend sufficient time working with engaging applications, without losing focus on the Major Work of each grade. How to Find the Evidence: Select one or more cluster(s) or Standard(s) from the Major Work for the grade being evaluated that relate specifically application to use throughout the questions associated with this metric. NOTE: Some examples of clusters or Standards that call for application include: K.OA.A.2, 1.OA.A, 2.OA.A, 3.OA.A.3, 3.OA.D.8, 4.OA.A.3, 4.NF.B.3d, 4.NF.B.4c, 5.NF.B.6, 5.NF.B.7c, 6.RP.A.3, 6.NS.A.1, 6.EE.B.7, 6.EE.C.9, 7.RP.A, 7.NS.A.3, 7.EE.B.3, 8.EE.C.8c, 8.F.B For context, read Criterion #4c in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Are there are single- and multi-step contextual problems, including non-routine problems, that develop the mathematics of the grade, afford opportunities for practice, and engage students in problem solving? Do the problems attend thoroughly to those places in the content Standards where expectations for multi-step and real-world problems are explicit? Do application problems particularly stress applying the Major Work of the grade? Does modeling build slowly across K–8, with applications that are relatively simple in earlier grades and when students are encountering new content? In grades 6–8, do the problems begin to provide opportunities for students to make their own assumptions or simplifications in order to model a situation mathematically?





Rating: (Reviewer)

Are there are single- and multi-step contextual problems, including non-routine problems, that develop the mathematics of the grade, afford opportunities for practice, and engage students in problem solving? Do the problems attend thoroughly to those places in the content Standards where expectations for multi-step and real-world problems are explicit? Evaluate lessons, chapter/unit assessments, and homework assignments.

Evidence- Connected Mathematics 3 provides a plethora of opportunities for students to work with engaging applications; in fact, that is one of the defining features of the program. Each lesson is introduced with a contextual, non-routine problem which is then investigated using the concepts and skills learned in the current lesson. Then, these concepts and skills are integrated into the students’ problem-solving strategies and skills sets, to be applied to problem-solving situations encountered in the future. The ACE assignment at the conclusion of each investigation includes single and multi-step contextual problems which range from procedural practice to simple real-world applications to problems which require some thought and reasoning. One can examine any ACE problem set in the program and find a wealth of opportunities for practice and problem solving.


Do application problems particularly stress applying the Major Work of the grade? Evaluate lessons, chapter/unit assessments, and homework assignments. NOTE: Examples of evaluating this Criterion might include looking at: how well, by the end of grade 2, students using the materials as designed can represent and solve a full range of one-step addition and subtraction word problems; or how well, by the end of grade 3, students using the materials as designed can represent and solve a full range of one-step multiplication and division word problems; or how well these basic situation types for each operation are carried coherently across the grades, (e.g., with fractions and algebraic expressions); or, in all grades, whether the problems connect concepts, Standards, and domains in ways that are natural and important. For a list of situation types for one-step addition, subtraction, multiplication, and division problems, see Situation Types for the Operations in Word Problems

Evidence- Each investigation within each unit of Connected Mathematics 3 is correlated to a series of Common Core standards, with the vast majority of these standards being components of the Major Clusters. The ACE problem set at the end of each investigation definitely develops students’ conceptual understanding and skill development related to the Major Work of the grade. For example, the ACE problems in Growing, Growing, Growing and Say It with Symbols contain application, connection, and extension problems that explore all of the following 8th Grade Common Core standards for Functions. With the addition of Frogs and Fleas and Painted Cubes and Function Junction, the Algebra Common Core Standards for Functions are covered, as well.





Rating: (Reviewer)

Does modeling build slowly across K–8, with applications that are relatively simple in earlier grades and when students are encountering new content? In grades 6–8, do the problems begin to provide opportunities for students to make their own assumptions or simplifications in order to model a situation mathematically? Read Standard for Mathematical Practice 4, Model with Mathematics. Evaluate lessons, chapter/unit assessments, and homework assignments.

Evidence- In Connected Mathematics 3, mathematical modeling is employed as an instructional strategy and as a learning strategy throughout the course. In Grade 8, an entire unit is devoted to Thinking with Mathematical Models, but modeling problem situations with words, pictures, graphs, tables, expressions, and equations is prevalent in all of Grades 6-8 and Algebra. Mathematical Practice 4: Model with Mathematics is used by students and teachers in virtually every lesson, and some investigations feature this particular practice in their Mathematical Reflections (e.g., Growing, Growing, Growing, Investigation 3, page 59).


AC1 Rating ____Meets ____Does Not Meet





Rating: (Reviewer)

Strengths:

Weaknesses:




Rating: (Reviewer)

Alignment Criterion 2: Standards for Mathematical Practice Materials must demonstrate authentic connections between content Standards and practice Standards.

Required Materials: • Common Core State Standards for Mathematics (http:// corestandards.org/wp-content/uploads/Math_Standards.pdf) • Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013) (http://www. corestandards.org/wp-content/uploads/Math_Publishers_ Criteria_K-8_Spring_2013_FINAL1.pdf) • Focus by Grade Level for the grade being evaluated (www. achievethecore.org/focus) • From the materials being evaluated: teacher guides, student texts and workbooks

Rating this Criterion Alignment Criterion 2 is rated as Meets or Does Not Meet. To rate Alignment Criterion 2, first rate metrics 2A, 2B, and 2C. Rate each metric as Meets (2 points), Partially Meets (1 point), or Does Not Meet (0 points). For each metric, guiding questions are provided to aid in gathering evidence. Since there are three metrics, and each metric is worth up to 2 points, the maximum possible rating across all three metrics is 6 points. Ideally, aligned materials will earn all 6 points; materials are judged to have met Alignment Criterion 2 if the materials earn 5 or 6 points. This threshold recognizes that evaluators sometimes differ in how they assess features such as mathematical practices, while at the same time ensuring that no single metric can receive a rating of zero and be aligned to the Shifts and major features of the CCSSM.




Rating: (Reviewer)

Metric AC2A: Materials address the practice Standards in such a way as to enrich the Major Work of the grade; practices strengthen the focus on Major Work instead of detracting from it, in both teacher and student materials. How to Find the Evidence: Familiarize yourself with the Major Work of the grade being evaluated (see the Focus by Grade Level documents.) Evaluate teacher and student materials for evidence that the mathematical practices support and connect to the focus of the grade. NOTE: Examples of evaluating this Criterion might include looking at whether, in grades K–5, students using the materials are supported to look for and express regularity in repeated reasoning about the addition table, the multiplication table, the properties of operations, the relationship between addition and subtraction or multiplication and division, and the place value system; or whether, in grades 6–8, students using the materials are supported to look for and express regularity in repeated reasoning about proportional relationships and linear functions. For context, read Criterion #8 in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Evidence of adherence to Mathematical Practices is abundant in all grade levels throughout the Connected Mathematics 3 program. All of the Mathematical Practices are cited at the beginning of each unit, including a bulleted list of smaller tasks for each practice which students can consider during the course of the unit as they focus on making these practices regular Habits of Mind as they explore and internalize the concepts of the Major Clusters of their grade. At the conclusion of each investigation, Mathematical Reflections include an example of how a particular Mathematical Practice was employed by a (fictional) student to solve a problem. The activity requires the CMP3 student to identify other Mathematical Practices used in the solution of the problem, and to identify a problem within the recently completed investigation which involved a particular Mathematical Practice in the solution process. Example: In the Mathematical Reflections for Frogs, Fleas, and Painted Cubes, Investigation 3, students read an example of a solution strategy using Mathematical Practice 2: Reason abstractly and quantitatively.


Metric AC2B: Materials attend to the full meaning of each practice Standard. How to Find the Evidence: For context, read Criterion #7 and Criterion #9 in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Over the course of any given year of instruction, is each mathematical practice Standard meaningfully present in the form of assignments, activities, or problems that stimulate students to develop the habits of mind described in the practice Standard? Do the materials treat the practice Standards as developing across grades or grade bands? Are the practice Standards in early grades appropriately simple? Do they display an arc of growing sophistication across the grades? Are there teacher-directed materials that explain the role of the practice Standards in the classroom and in students’ mathematical development? Are alignments to practice Standards accurate?





Rating: (Reviewer)

Over the course of any given year of instruction, is each mathematical practice Standard meaningfully present in the form of assignments, activities, or problems that stimulate students to develop the habits of mind described in the practice Standard? Evaluate lessons, chapter/ unit assessments, and homework assignments for evidence of each mathematical practice being meaningfully present in instruction.

Evidence- Evidence of adherence to Mathematical Practices is abundant in all grade levels throughout the Connected Mathematics 3 program. All of the Mathematical Practices are cited at the beginning of each unit, including a bulleted list of smaller tasks for each practice which students can consider during the course of the unit as they focus on making these practices regular Habits of Mind. At the conclusion of each investigation, Mathematical Reflections include an example of how a particular Mathematical Practice was employed by a (fictional) student to solve a problem. The activity requires the CMP3 student to identify other Mathematical Practices used in the solution of the problem, and to identify a problem within the recently completed investigation which involved a particular Mathematical Practice in the solution process. Example: In the Mathematical Reflections for Butterflies, Pinwheels, and Wallpaper, Investigation 2, students read an example of a solution strategy using Mathematical Practice 6: Attend to precision.


Do the materials treat the practice Standards as developing across grades or grade bands? Are the practice Standards in early grades appropriately simple? Do they display an arc of growing sophistication across the grades?

Evidence- Evidence of adherence to Mathematical Practices is abundant in all grade levels throughout the Connected Mathematics 3 program. All of the Mathematical Practices are cited at the beginning of each unit, including a bulleted list of smaller tasks for each practice which students can consider during the course of the unit as they focus on making these practices regular Habits of Mind. At the conclusion of each investigation, Mathematical Reflections include an example of how a particular Mathematical Practice was employed by a (fictional) student to solve a problem. The activity requires the CMP3 student to identify other Mathematical Practices used in the solution of the problem, and to identify a problem within the recently completed investigation which involved a particular Mathematical Practice in the solution process. Example: In the Mathematical Reflections for Looking for Pythagoras, Investigation 1, students read an example of a solution strategy using Mathematical Practice 5: Use appropriate tools strategically.





Rating: (Reviewer)

Are there teacher-directed materials that explain the role of the practice Standards in the classroom and in students’ mathematical development? Are alignments to practice Standards accurate?

Evidence- Evidence of adherence to Mathematical Practices is abundant in all grade levels throughout the Connected Mathematics 3 program. All of the Mathematical Practices are cited at the beginning of each unit, including a bulleted list of smaller tasks for each practice which students can consider during the course of the unit as they focus on making these practices regular Habits of Mind. At the conclusion of each investigation, Mathematical Reflections include an example of how a particular Mathematical Practice was employed by a (fictional) student to solve a problem. The activity requires the CMP3 student to identify other Mathematical Practices used in the solution of the problem, and to identify a problem within the recently completed investigation which involved a particular Mathematical Practice in the solution process. Example: In the Mathematical Reflections for Growing, Growing, Growing, Investigation 3, students read an example of a solution strategy using Mathematical Practice 4: Model with Mathematics.


Metric AC2C: Materials support the Standards’ emphasis on mathematical reasoning. How to Find the Evidence: For context, read Criterion #10 in the Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013).

Evidence- Do the materials support students in constructing viable arguments and critiquing the arguments of others concerning grade-level mathematics that is detailed in the content Standards? Do the materials support students in producing not only answers and solutions, but also, in a grade-appropriate way, arguments, explanations, diagrams, mathematical models, etc., especially in the Major Work of the grade? Do materials explicitly attend to the specialized language of mathematics? Is the language of argument, problem solving, and mathematical explanations taught rather than assumed?





Rating: (Reviewer)

Do the materials support students in constructing viable arguments and critiquing the arguments of others concerning grade-level mathematics that is detailed in the content Standards? Read Standard for Mathematical Practice 3. Evaluate teacher and student materials to ensure that students are given opportunities to reason with grade-level mathematics.

Evidence- Mathematical reasoning is practiced by CMP3 students throughout the program. Students analyze and critique the reasoning of others, find errors in samples of students’ mathematical arguments, identify the Mathematical Practice employed in a student’s explanation of his or her solution strategy, explain their own reasoning and solution strategies, and engage in cooperative learning groups to discuss mathematical reasoning and strategies for arriving at an agreed-upon solution. Almost all of the problems in the ACE assignments at the end of each investigation require some level of mathematical reasoning on the part of the student, and many require the student to explain his or her reasoning.


Do the materials support students in producing not only answers and solutions, but also, in a grade-appropriate way, arguments, explanations, diagrams, mathematical models, etc., especially in the Major Work of the grade? Familiarize yourself with the Major Work of the grade being evaluated (see the Focus by Grade Level documents.) Evaluate teacher and student materials, to understand the types of work students are expected to produce.

Evidence- Mathematical modeling is present in some form in every unit of Connected Mathematics 3. When students write number sentences; create symbolic expressions; represent a mathematical problem with a table, graph, or equation; or draw a diagram to describe the constraints to help them understand and solve a contextual problem situation, they are creating a mathematical model of the situation. Similarly, as described above, students identify, critique, practice, and verbalize mathematical reasoning as they solve problems, independently or in groups, presented in the instructional pages and the ACE assignments for each investigation.


Do materials explicitly attend to the specialized language of mathematics? Is the language of argument, problem solving, and mathematical explanations taught rather than assumed? Evaluate teacher and student materials, paying attention to how mathematical language is taught. NOTE: Examples of evaluating this Criterion might include looking at whether students are supported in: basing arguments on definitions; using the method of providing a counterexample; or recognizing that examples alone do not establish a general statement.

Evidence- Each unit includes a glossary of mathematical vocabulary. Specialized mathematical terms are bold-faced in the student textbook. In the teacher resources, teachers are encouraged to foster the use of precise mathematical language by directing students to circle or underline important terms in the text, to create and maintain a word cluster or vocabulary chart in the classroom and in students’ notebooks, to practice reading and speaking mathematical text, to encourage students to write clear and accurate explanations for the ACE problems, and to guide classroom discussions using appropriate and precise mathematical terminology.





Rating: (Reviewer)


Comments: (be specific)





Rating: (Reviewer)

Alignment Criterion 3: Access to the Standards for All Students Materials must provide supports for English Language Learners and other special populations.

Required Materials:

• Common Core State Standards for Mathematics (http:// corestandards.org/wp-content/uploads/Math_Standards.pdf) • Publishers’ Criteria for the Common Core State Standards for Mathematics, Grades K–8 (Spring 2013) (http://www. corestandards.org/wp-content/uploads/Math_Publishers_ Criteria_K-8_Spring_2013_FINAL1.pdf) • From the materials being evaluated: teacher guides, student

texts and workbooks

Rating this Criterion: Alignment Criterion 3 is rated as Meets or Does Not Meet. To rate Alignment Criterion 3, first rate metrics 3A, 3B, and 3C. Rate each metric as Meets (2 points), Partially Meets (1 point), or Does Not Meet (0 points). Since there are three metrics, and each metric is worth up to 2 points, the maximum possible rating across all three metrics is 6 points. Ideally, aligned materials will earn all 6 points; materials are judged to have met Alignment Criterion 3 if the materials earn 5 or 6 points. This threshold recognizes that evaluators sometimes differ in how they assess features such as support for special population, while at the same time ensuring that no single metric can receive a rating of zero and be aligned to the Shifts and major features of the CCSSM.




Rating: (Reviewer)

Metric AC3A: Support for English Language Learners and other special populations is thoughtful and helps those students meet the same Standards as all other students. The language in which problems are posed is carefully considered. How to Find the Evidence: Evaluate teacher and student materials, paying attention to supports offered for special populations.

Evidence- English Language Learners are served by creating a friendly, supportive, and predictable classroom community; employing modeling and other means of communicating mathematical ideas; and fostering active participation with effective questioning and working in cooperative groups. The teacher support materials include a section called, “Providing for Individual Needs,” which gives teachers ideas for supporting individual student needs and providing differentiated instruction. For students who require more advanced work, open-ended questions stimulate divergent thinking and provide students with opportunities to express their reasoning. Extensions in the ACE assignments often explore beyond what was directly covered in the classroom. In the teacher support materials, there are questions in the Launch-Explore-Summarize features that are labeled, “Going Further.” These questions would be appropriately posed to students who are able to advance beyond the basic curriculum.


Metric AC3B: Materials provide appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners with gradual removal of supports, when needed, to allow students to demonstrate their mathematical understanding independently. How to Find the Evidence: Evaluate teacher and student materials, paying attention to whether materials provide differentiation that will lead all learners to engage with on-grade-level content.

Evidence-

The CMP3 program provides an appropriate level and type of scaffolding, differentiation, intervention and support for a broad range of learners. The curriculum supports diverse cultural and linguistic backgrounds, interests, and lifestyles. The materials and teacher resources include extra supports for students working below grade level, as well as extensions for students with high interest or who are working above grade level.

The teacher support materials include a section called, “Providing for Individual Needs,” which gives teachers ideas for supporting individual student needs and providing differentiated instruction.

The needs of students who have been identified as gifted or who require advanced work are served by problems which vary in complexity and the organization of content around concepts and abstract ideas. Problems promote higher levels of thinking by emphasizing use over acquisition of information. Open-ended questions stimulate divergent thinking and provide students with opportunities to express their reasoning. Extensions in the ACE assignments often explore beyond what was directly covered in the classroom. In the teacher support materials, there are questions in the Launch-Explore-Summarize features that are labeled, “Going Further.” These questions would be appropriately posed to students who are able to advance beyond the basic curriculum.





Rating: (Reviewer)

Metric AC3: Design of lessons recommends and facilitates a mix of instructional approaches for a variety of learners such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share). How to Find the Evidence: Evaluate teacher materials, noting instructional approaches suggested for whole class and differentiated lessons and activities.

Evidence- The extensive field testing performed for CMP3 helped produce teacher materials rich with successful strategies, illustrative classroom dialogues and questions, and examples of student solutions and reasoning. The Teacher's Guide for each unit contains a discussion of the mathematics underlying the Investigations, mathematical and problem-solving goals for each Investigation, connections to other units, in-depth teaching notes, and an extensive assessment package. Mathematical modeling is present in some form in every unit of Connected Mathematics 3. When students write number sentences; create symbolic expressions; represent a mathematical problem with a table, graph, or equation; or draw a diagram to describe the constraints to help them understand and solve a contextual problem situation, they are creating a mathematical model of the situation. The needs of all learners are served by problems which vary in complexity and the organization of content around fundamental concepts and abstract ideas. Open-ended questions stimulate divergent thinking and provide students with opportunities to express their reasoning. Cooperative learning groups enable students of all ability levels to participate productively in the learning process by listening to the strategies of their classmates and by contributing meaningfully to the discussion and sharing their own ideas.







Rating: (Reviewer)


Indicators of Quality- Adapted from Instructional Materials Evaluation Toolkit (IMET)

Evidence- Include a narrative explanation. Be specific.

Rating:

1. Lessons are thoughtfully structured and support the teacher in leading the class through the learning paths at hand, with active participation by all students in their own learning and in the learning of their classmates.

Evidence- Lessons are organized in the teacher support materials in a Launch-Explore-Summarize structure which enables the teacher to provide support to students who require more explanation and to enhance the learning of advanced students by providing more challenging problems. Sample reference: Say It with Symbols Teacher’s Guide, Lesson 3.2, pages 160-164

______ Yes ______ No

2. The underlying design of the materials includes both problems and exercises. (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. NOTE: This Criterion does not require that the problems and exercises be labeled as such.

Evidence- ACE problems at the conclusion of each investigation include exercises which require procedural skill and problems which require analysis, reasoning, and strategy. Sample reference: Thinking with Mathematical Models, Investigation 3, pages 69-78

______ Yes ______ No

3. Design of assignments is not haphazard: exercises are given in intentional sequences in order to strengthen students’ mathematical understanding.

Evidence- The ACE assignments progress from Applications to Connections to Extensions. They are organized sequentially so as to provide increasing challenge and require deeper understanding as a student progresses through the assignment. Teachers have the option of thoughtfully assigning subsets of these problems. Sample reference: Thinking with Mathematical Models, Investigation 3, pages 69-78

______ Yes ______ No

4. There are separate teacher materials that support and reward teacher study including, but not limited to: discussion of the mathematics of the units and the mathematical point of each lesson as it relates to the organizing concepts of the unit, discussion on student ways of thinking and anticipating a variety of students responses, guidance on lesson flow, guidance on questions that prompt students thinking, and discussion of desired mathematical behaviors being elicited among students.

Evidence- Teacher support materials include A Guide to Connected Mathematics 3 which provides an overview of the program, including its philosophical underpinnings, and contains correlations of components of the program to Common Core standards. Each grade level includes a book of Teacher Resources which includes a variety of assessments and Labsheets as well as a parent letter for each unit.

______ Yes ______ No



Rating:

5. Manipulatives suggested in the materials are faithful representations of the mathematical objects they represent and are connected to written methods.

Evidence- A wide variety of manipulatives to facilitate visual and physical modeling of math problems is available for use with Connected Mathematics 3. Materials required for each lesson are listed in the Teachers Guide for the appropriate unit. Sample reference: Sample reference: A Guide to Connected Mathematics 3, pages 40-41

______ Yes ______ No

6. Materials include a variety of curriculum-embedded assessments. Examples include pre-, formative, summative, and self-assessment resources.

Evidence- Assessments provided to the teacher in the Teacher Resources book for each grade include two Check Ups, a Partner Quiz, a Unit Test (correlated to the unit problems), a Self Assessment, and a Notebook Checklist. Teachers are encouraged to perform ongoing informal assessment in the classroom as necessary.

______ Yes ______ No

7. Assessments contain aligned rubrics, answer keys, and scoring guidelines that provide sufficient guidance for interpreting student performance.

Evidence- The Teacher Resources book for each grade contains solutions to all of the assessment forms provided. A Notebook Checklist enables the student and teacher to keep track of individual progress toward completing a unit.

______ Yes ______ No

8. Materials assess student proficiency using methods that are accessible and unbiased, including the use of course-level language in student prompts.

Evidence- The variety of assessment forms available to the instructor provides an opportunity for an unbiased and multifaceted rubric for assessing student proficiency.

______ Yes ______ No

9. Materials are carefully evaluated by qualified individuals, whose names are listed, in an effort to ensure freedom from mathematical errors and course-level appropriateness.

Evidence- The Team of Experts who wrote the CMP3 textbooks are listed in A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching. The extensive research that went into the preparation and evaluation of the CMP3 materials is also outlined in the Guide.

______ Yes ______ No



Rating:

10. The visual design supports students in engaging thoughtfully with the subject. Navigation through the text is clear.

Evidence- The student textbook is visually appealing with strategically arranged text, bold-faced and colored fonts, and appropriate illustrations that facilitate a close reading and understanding of the text. Sample reference: Butterflies, Pinwheels, and Wallpaper, Lesson 1.2, pages 12-14

______ Yes ______ No

11. The materials engage parents in appropriate ways. For example, homework assignments in elementary grades, consist of routine problems, practice with getting answers, and fluency-building exercises that parents can easily support.

Evidence- The textbook is written at the appropriate grade level, so parents will be able to read and understand the material. The mathematics is applied in real-life contexts, so parents will be able to relate to the problem situations and talk about them with their children. In addition, a sample parent letter for each unit is included in the Teacher Resources book, communicating the mathematics that will be learned by their children in the upcoming days and weeks. Sample reference: Teacher Resources, Grade 8, pages 5-8

______ Yes ______ No

The IMET was developed by Student Achievement Partners. Educators may use or adapt.

Adapted from Instructional Materials Evaluation Toolkit (IMET)

Standards Alignment Evaluation Rubric 0 = No Alignment– Not Evident: ELA/Literacy content as described in the Standards is not evident. .5 = Partial Alignment- Partially Evident: ELA/Literacy content as described in the Standards is partially evident and there are few gaps. 1 = High Alignment – Clearly Evident: ELA/Literacy content is fully aligned as described in the Standards and repeatedly included to guarantee extensive opportunities for students to work with the content. Alignment is clearly evident. N/A = Not applicable for standard.

ELA/Literacy in Science & Technical Subjects Grade 6-8

ANCHOR STANDARD: Key Ideas and Details Grade 6-8 Objectives

Provider: List units with specific examples of where standards are

Introduced/Taught/Assessed. Include a narrative explanation.

Point Value 0/.5/1

(Reviewer)

CCRA.R.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

The student materials for the entire Connected Mathematics 3 program are written at grade-level to facilitate close reading and understanding of the vocabulary, instruction, problems, practice, and review content. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

CCRA.R.2 Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

RST.6-8.2 Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.

Central ideas presented in Connected Mathematics 3 are outlined at the beginning of each unit and investigation. Important vocabulary words are printed in a bold-faced font. Problems are clearly labeled and separated from instructional text. The spatial organization of the page facilitates close reading and understanding of the content. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

CCRA.R.3 Analyze how and why individuals, events, and ideas develop and interact over the course of a text.

RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Instructors practice ongoing assessment strategies to verify student comprehension, mastery, and readiness to proceed. Group activities and labs are supervised by the teacher, who can observe student adherence to precision and accuracy when solving a multi-step problem or collaborating on a unit project. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

ANCHOR STANDARD: Craft and Structure

Grade 6-8 Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.R.4 Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meaning or tone.

RST.6-8.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.

With clear writing and teacher guidance, students are able to interpret mathematical words and phrases and understand and be able to solve given problem situations. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

CCRA.R.5 Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

RST.6-8.5 Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to an understanding of the topic.

Titles, subtitles, headings, and differences in font color and style enable the student to readily identify instruction, problems, projects, and homework assignments. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text.

RST.6-8.6 Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text.

The point of view of the math textbook materials is objective and unbiased and, as much as possible, written from the perspective of a student at grade level. The content of the problems is of interest to a student at grade level. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

ANCHOR STANDARD: Integration of Knowledge

and Ideas Grade 6-8

Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.R.7 Integrate and evaluate content presented in diverse formats and media, including visually and quantitatively, as well as in words.

RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

Mathematical information is modeled with words, tables, graphs, and illustrations. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

CCRA.R.8 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

RST.6-8.8 Distinguish among facts, reasoned judgment based on research findings, and speculation in a text.

Problem situations are contextual and are based on real-world scenarios. Some problems present reasoning samples to be critiqued. In these situations, students must distinguish between valid and invalid reasoning and identify technical errors. Sample reference: Growing, Growing, Growing, Investigation 5, ACE #1, page 88

CCRA.R.9 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

RST.6-8.9 Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

When writing Mathematical Reflections and completing Unit Projects, students have an opportunity to view problem situations from multiple perspectives, including their own. This provides the best opportunity for comparing and contrasting information from the text with their own experiences and perspectives. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page35

ANCHOR STANDARD: Range of Reading and

Level of Text Grade 6-8

Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.R.10 Read and comprehend complex literary and informational texts independently and proficiently.

RST.6-8.10 By the end of grade 8, read and comprehend science/technical texts in the grades 6–8 text complexity band independently and proficiently.

The Connected Mathematics 3 text materials are written at grade level, and students are able to closely read and interpret the content so that they can solve the problems presented in the text and in the ACE assignments. Sample reference: Growing, Growing, Growing, Investigation 4, pages 60-75

*#3 Note: Students’ narrative skills continue to grow in these grades. The Standards require that students be able to incorporate narrative elements effectively into arguments and informative/explanatory texts. In history/social studies, students must be able to incorporate narrative accounts into their analyses of individuals or events of historical import. In science and technical subjects, students must be able to write precise enough descriptions of the step-by-step procedures they use in their investigations or technical work that others can replicate them and (possibly) reach the same results. *

ANCHOR STANDARD: Text Types and Purposes Grade 6-8 Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.

WHST.6-8.1 Write arguments focused on discipline-specific content. a. Introduce claim(s) about a topic or issue, acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. b. Support claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources. c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. d. Establish and maintain a formal style. e. Provide a concluding statement or section that follows from and supports the argument presented.

Students write arguments as they complete the Mathematical Reflections at the conclusion of each investigation. They also have opportunities to write arguments as they explain or justify their reasoning, or critique the reasoning of others, when solving problems. Sample reference: Thinking with Mathematical Models, Investigation 2, Mathematical Reflections, page 59

CCRA.W.2 Write informative/ explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

WHST.6-8.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples. c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts. d. Use precise language and domain-specific vocabulary to inform about or explain the topic. e. Establish and maintain a formal style and objective tone.f. Provide a concluding statement or section that follows from and supports the information or explanation presented.

Students write informative and explanatory texts as they solve multi-step problems and explain their solution strategies, and as they prepare their Unit Project presentations. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

CCRA.W.3 Write narratives to develop real or imagined experiences of events using effective technique, well, chosen details and well-structured event sequences.

WHST.6-8.3 (See note; not applicable as a separate requirement)

Students have the freedom to write creatively as they complete the Mathematical Reflections at the end of each investigation. Sample reference: Thinking with Mathematical Models, Investigation 2, Mathematical Reflections, page 59

ANCHOR STANDARD: Production and Distribution of Writing

Grade 6-8 Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

WHST.6-8.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Students are encouraged to produce clear and coherent writing as they develop mathematical arguments and explain their reasoning, as they critique the reasoning of others, and as they prepare more lengthy responses to Mathematical Reflections and Unit Project presentations. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

CCRA.W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

WHST.6-8.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed.

Students are able to develop and strengthen their writing as they outline mathematical arguments and explain their reasoning, as they critique the reasoning of others, and as they prepare more lengthy responses to Mathematical Reflections and Unit Project presentations. Peer review and teacher feedback can also facilitate development in writing. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

CCRA.W.6 Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

WHST.6-8.6 Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently.

CMP3 students and teachers will have access to a Pearson MathXL account. Students can interact with digital pages to complete homework assignments or submit written work to their teachers for review or to share with other students in the class.

ANCHOR STANDARD: Research to Build and

Present Knowledge Grade 6-8

Objectives



Point Value 0/.5/1

(Reviewer)

CCRA.W.7 Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Students complete Unit Projects. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

CCRA.W.8 Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.

WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

Students gather relevant information as they complete Unit Projects and respond to Mathematical Reflections. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

CCRA.W.9 Draw evidence from literary or informational texts to support analysis, reflection, and research.

WHST.6-8.9 Draw evidence from informational texts to support analysis reflection, and research.

Students can draw evidence from outside sources as they complete Unit Projects. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

ANCHOR STANDARD: Range of Writing

Grade 6-8

Objectives Provider: List units with specific examples of where standards are


Point Value 0/.5/1

(Reviewer)

CCRA.W.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

WHST.6-8.10 Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

Students write over extended time frames as they respond to Mathematical Reflections and complete Unit Projects. Students write over shorter time frames as they prepare responses to ACE assignments and participate in cooperative learning groups. Sample reference: Growing, Growing, Growing Teacher’s Guide, Unit Project, page 35

Please double check the material’s alignment to standards.

Alignment to Idaho Content Standards: _____% correlation

**If the material aligns to the Idaho Content Standards with at least an 80%, move on to: Material Analysis. If the material has

less than an 80% alignment, please notify your team leader.

Material Analysis:

Student Focus Comments/Examples

(Publisher and Reviewer)

Point Value

(Reviewer)

0 = Not Evident

.5 = Partially Evident

1 = Clearly Evident

N/A = Not applicable for standard.

1. The material supports the sequential and cumulative development of foundational skills. Those skills are necessary for a student’s independent comprehension of grade-level complex texts and mastery of tasks called for by the standards.

CMP3’s development was guided by the notion that all students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of mathematics. This includes the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency. Sample reference: A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching

2. The material provides many and varied opportunities for students to work with each standard within the grade level.

The richness of the problems presented in CMP3 offers robust opportunities for students to engage in both major and supporting content in each grade level. This interweaving of content from different domains and clusters is a hallmark of the program. Sample reference: A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


3. The material reflects the progression of the strands and how they build within and across the grades in a logical way. This enables students to develop and demonstrate their independent capacity to read and write at the appropriate level of complexity and sophistication indicated by the standards.

The content progressions in CMP3 align to the progressions in the Standards. Students make tangible progress each year with minimum review. In CMP3, grade level work begins during the first two to four weeks. Sample reference: A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching

4. The material engages the reader, i.e. Does it correspond with age appropriate interests?

CMP3 is built on a foundation of inquiry-based instruction that has sense-making and problem-solving at its heart. The structure of the program encourages students to engage in mathematical discourse as they present and defend their solutions. Sample reference: Looking for Pythagoras, Explain Your Reasoning, pages 106-107

5. The material cross-refers and integrates with other subjects in related areas of the curriculum.

The content provides natural applications to other disciplines, including science, history, and the arts. Sample reference: Looking for Pythagoras, Lesson 3.4, page 46-48

6. The material includes strategies and textual content that are grade appropriate.

The structure of the CMP3 program provides students with extensive work with grade-level problems. Rather than asking students to spend important classroom time with a series of skills practice exercises, CMP3 asks them to ponder solutions to rich problems that require them to draw on concepts and skills that are grade-level appropriate. Sample reference: Growing, Growing, Growing, Investigation 3, Extensions, pages 56-57



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


7. The material has a balance of text types and lengths that encourage close, in-depth reading and rereading, analysis, comparison, and synthesis of texts.

CMP3 encourages higher-order thinking processes and open-ended investigations through evaluation and analyzing of texts and other resources. Students are prompted to communicate effectively by reading, writing, listening, speaking and thinking mathematically. Sample reference: Growing, Growing, Growing, Investigation 3, pages 42-59

8. The material includes sufficient supplementary activities or assignments that are appropriately integrated into the text.

The tasks and assignments in CMP3 ask students to produce a range of solutions, from calculations and computations to models and written explanations. For example, each investigation ends with a Mathematical Reflection in which students record their thinking about their work from the investigation. Sample reference: Looking for Pythagoras, Investigation 2, Mathematical Reflections, page 36

9. The material has activities and assignments that develop problem-solving skills and foster synthesis and inquiry at both an individual and group level.

Critical thinking, problem solving, and communication are at the core of the CMP3 pedagogy. Students develop an understanding of important mathematical ideas by solving problems and reflecting on the mathematics involved. Every day, students use “habits of mind” to make sense of problems and apply what they learn to new situations. Sample reference: Growing, Growing, Growing, Investigation 3, pages 42-59



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


10. The material has activities and assignments that reflect varied learning styles of students.

CMP3 establishes high expectations for all students, and supports learners at either end of the learning spectrum. CMP3 has been successfully implemented in classrooms, addressing diverse student needs in the mathematics classroom, including those with special needs. Students have increased opportunities to engage in cooperative learning, to take on leadership roles, and to cultivate self-esteem and self-acceptance. Sample reference: Growing, Growing, Growing, Investigation 3, pages 42-59

11. The material includes appropriate instructional strategies.

The CMP teacher materials are organized around an instructional model that supports inquiry-based teaching. The CMP model looks at instruction in three phases: launching, exploring, and summarizing. Specific notes and questions for each problem are provided in the teacher support. Sample reference: Growing, Growing, Growing Teacher’s Guide, Investigation 3, pages 132-157

Pedagogical Approach Comments/Examples


Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


12. The material offers strategies for teachers to meet the needs of a range of learners, including advanced students and those requiring remediation.

The extensive field testing performed for CMP3 helped produce teacher materials rich with successful strategies, illustrative classroom dialogues and questions, and examples of student solutions and reasoning. The Teacher's Guide for each unit contains a discussion of the mathematics underlying the Investigations, mathematical and problem-solving goals for each Investigation, connections to other units, in-depth teaching notes, and an extensive assessment package. Sample reference: A Guide to Connected Mathematics 3: Providing for Individual Needs, page 85; A Curriculum for All Students, pages 94-111

13. The material provides suggestions for scaffolding that support the comprehension of grade-level text without replacing students’ opportunities for full and regular encounters with grade-level complex texts. Removing the scaffolding over the course of the materials is encouraged.

CMP3 provides an appropriate level and type of scaffolding, differentiation, intervention and support for a broad range of learners. The program supports diverse cultural and linguistic backgrounds, interests, and lifestyles. CMP3 provides extra supports for students working below grade level and extensions for students with high interest or working above grade level. Sample reference: A Guide to Connected Mathematics 3: Providing for Individual Needs, page 85; A Curriculum for All Students, pages 94-111



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


14. The material provides opportunities for supporting English language learners to regularly and actively participate with grade-level text.

Strategies to use with English Language Learners, and other “special populations,” are not explicitly labeled as such, because these strategies will benefit many different types of student learners, not just the ELL or other “labeled” populations. By integrating these strategies throughout the program, teachers can use them for broader, more appropriate, and more effective use, in order to target individual student needs. This allows teachers to focus on differentiating instruction for each student individually, addressing the student’s personal needs, rather than addressing a label associated with the student. Sample reference: A Guide to Connected Mathematics 3: Providing for Individual Needs, page 85; A Curriculum for All Students, pages 94-111

15. The material offers texts representing a wide array of cultures and experiences, allowing students opportunities to learn about situations similar to and different from their own personal experiences.

Pearson has systematically developed its educational products to incorporate criteria and standards that reflect multiethnic, multiracial, and multicultural perspectives. Over the years, the publisher has worked with numerous experts and consultants from universities and other educational institutions to provide a broad perspective from the most respected experts in their fields.



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


While creating the very best educational content, Pearson’s standards are aimed at the following:

Integrating multicultural experiences into program content so students see themselves as part of what is valued in the school’s curriculum

Fostering self-esteem for greater academic achievement

Empowering students to act effectively in a democratic society and reach their full potential

Reducing prejudice by showing multicultural friendships and people from different backgrounds working, playing, and living together

Sample references: Say It with Symbols, Investigation 3, page 55; A Guide to Connected Mathematics 3: Providing for Individual Needs, page 85; A Curriculum for All Students, pages 94-111



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


16. The material provides a balanced representation of points of view regarding issues such as race, gender, religion, environment, business, industry, political orientation, careers and career choices.

It is important to consider the needs of all students. Pearson’s educational materials have a fair and balanced representation of members of various cultural groups, including racial, ethnic and religious groups, males and females, older people and people with disabilities. Pearson’s educational materials accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. The publisher involves members of diverse ethnic and cultural groups in the concept development of Pearson products as well as in the writing, editing, illustrating, and designing. Sample references: Say It with Symbols, Investigation 3, page 55; A Guide to Connected Mathematics 3: Providing for Individual Needs, page 85; A Curriculum for All Students, pages 94-111



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


17. The material gives clear and concise instruction to teachers and students. It is easy to navigate and understand.

Educators can depend on well organized, high quality ancillary/supplementary materials that enhance instruction. Of particular interest are CMP3’s easy-to-use mobile and computer-based tools, which help with classroom management and capture student work on the go. For example, ExamView® delivers a full suite of assessment tools, while MathXL® for School, which comes with CMP3, provides individualized skills practice. Social networking technology connects CMP3 teachers, while students benefit from interactive digital pages that allow for instantaneous sharing and effective group work. Sample references: Growing, Growing, Growing, Investigation 3, student textbook pages 42-59, Teacher’s Guide pages 132-157; A Guide to Connected Mathematics 3, pages 38-40



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


18. The material assesses students at a variety of knowledge levels (e.g., recall, inferencing/analyzing, reasoning, problem solving) centered on grade-level texts that are clearly aligned and measureable against the expectations of the CCSS.

Assessment in CMP3 is designed to collect data concerning the following three dimensions of student learning:

Content Knowledge. Teachers and students determining what students know and what they are able to do

Mathematical Disposition. Students responding well to mathematical challenges and developing self-confidence as learners and inventors of mathematics. Students understanding their teachers’ expectations, monitoring and reflecting on their own learning

Work Habits. Students showing a willingness to persevere, contributing to group tasks, and following tasks to completion—skills that can be applied to other content areas and real world situations

Sample reference: Teacher Resources, Grade 8



Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


19. The material offers ongoing, easily implemented, and varied assessments.

Assessments should clearly denote which standards are being emphasized. They should also include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Assessment in CMP3 is an extension of the learning process, as well as an opportunity to check what students can do. For this reason, the assessment in CMP is multidimensional, giving students many ways to demonstrate how they are making sense of the mathematics.

Sample reference: Teacher Resources, Grade 8

Technology Comments/Examples


Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


20. The material includes or references technology that provides teachers with additional tasks for students.

The CMP3 curriculum is available in a digital format online, organized along the following elements:

Teacher Place. Teacher Place facilitates planning, teaching, and classroom management. The online teacher dashboard, powered by Dash, allows users to interact with instructional content and student work in a flexible, personalized way.

Teachability.com. Teachability is a new community accessed via the Teacher Place. It lets CMP3 teachers collaborate with other CMP3 instructors. Teachers can share ideas, ask questions, offer tips, and get helpful strategies to improve student achievement.

Sample reference: A Guide to Connected Mathematics 3, pages 38-40

Technology Comments/Examples


Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


21. The material includes guidance for the mindful use of embedded technology to support and enhance student learning.

CMP3 incorporates a number of whiteboard-ready resources supporting interactivity in the mathematics classroom. These resources are found within the CMP3 online environment known as the Student Place. Teachers can project Student Place activities on an interactive whiteboard during class to make mathematical lessons come alive, including engaging videos and animations as well as powerful math tools and writing and drawing tools.

CMP3 has a suite of 12 digital math tools that students can access online as they work through problem solutions. There is also a problem (lesson)-based manipulatives kit for every grade. Many labsheets provide templates for creating paper manipulatives specific to a problem, such as the Shapes Set and the polystrips used in the unit Shapes and Designs. Sample reference: A Guide to Connected Mathematics 3, pages 38-40

Presentation and Design Comments/Examples (Publisher and Reviewer)

Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


22. The material has an aesthetically appealing appearance (attractive, inviting).

The clean design of CMP3 supports students in their learning by creating a non-distracting yet engaging visual environment.

Sample reference: Growing, Growing, Growing, Investigation 3, pages 42-59

23. The material has headings and sub-headings that make it easy to navigate through the book.

The design of CMP3 clearly distinguishes between problems and exercises. The Launch, Explore, and Summarize phases of each investigation are designed as learning experiences while the ACE exercises are practice exercises.


24. The material uses a language/reading level suitable for the intended readers.

The CMP3 authors from Michigan State University are well-respected math educators and active members of the NCTM community who have called on colleagues in the community to review the program at regular intervals. Because the program is so widely field-tested and researched, it is often reviewed and critiqued for mathematical accuracy and grade-level appropriateness.


Presentation and Design Comments/Examples (Publisher and Reviewer)

Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


25. The material has a reasonable and appropriate balance between text and illustration. The material has grade-appropriate font size.

CMP3 makes navigation easy and fun for students and teachers. Appropriately-proportioned text and illustrations enhance the learning experience.


26. The illustrations clearly cross-reference the text, are directly relevant to the content (not simply decorative), and promote thinking, discussion, and problem solving.

CMP3 promotes higher levels of thinking by stressing use of information found in text and illustrations rather than acquisition of information, as students continue to use information from previous Units in the current Unit they are studying.


Electronic/digital/online version Comments/Examples


Point Value

(Reviewer)

0 = Not Evident


1 = Clearly Evident


27. The material has “platform neutral” technology (i.e., will run on Windows or other platforms) and availability for networking.

The digital courseware for CMP3 is hosted by Pearson on its Realize platform. Pearson Realize is our newest learning management system. It is the online destination for standards-aligned content, flexible class management tools, and embedded assessments that deliver data to teachers instantly. It can run on Windows® 8, Windows 7, Mac OS X® 10.8.x, Mac OS X 10.7.x, iOS 8.0, iOS 7.0 (Apple iPad 2/3) on the following browsers: Microsoft® Internet Explorer 9, Microsoft Internet Explorer 10 (Desktop Only), Google® Chrome®, Apple® Safari®

(Mac®), and Mozilla Firefox®

The latest version of these browsers is supported; be sure the auto update feature is enabled.


28. The material has a user-friendly and interactive interface allowing the user to control (shift among activities).

Students benefit from interactive digital pages that allow for instantaneous sharing and effective group work.



STRENGTHS WEAKNESSES

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