Alignment: Overall Summary

The instructional materials reviewed for the Traditional series from Carnegie do not meet expectations for alignment to the CCSSM for high school. The materials partially meet the expectations for focus and coherence as they partially attend to the full intent of the mathematical content contained in the high school standards for all students, do not attend to the full intent of the modeling process when applied to the modeling standards, partially allow students to fully learn each standard, and partially identify and build on knowledge from Grades 6-8 to the High School Standards. The materials also partially meet the expectations for rigor and the MPs as they partially support the intentional development of conceptual understanding and do not meet the expectations for meaningfully connecting the MPs to the standards for mathematical content.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
11
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
11
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
11/18
+
-
Criterion Rating Details

The instructional materials partially meet the expectations for attending to the shifts of focus and coherence. The strength of the materials is the opportunity for students to learn the content that is widely applicable as prerequisites for post-secondary education. The series partially attends to a number of standards and did not meet expectations for having viable opportunities for students to engage in the modeling cycle. The context and real-life scenarios did meet expectations. The series did meet expectations for providing explicit and useful connections within and across courses, but it partially meets expectations for connections to mathematics from the middle grades.

Indicator 1a

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

Indicator 1a.i

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

The materials partially attend to the full intent of the mathematical content contained in the high school standards for all students. In most cases, the standard was addressed, clearly aligned and fully developed throughout the instructional materials. However, there were several instances where the instructional materials addressed the standard(s) to which it was aligned, but a particular component of the standard was not evident. In only a few instances were standards not clearly incorporated into the materials.

The following standards were identified as being especially strong/exemplary in terms of attending to the mathematical content:

  • F-IF.2: This standard is fully met. Function notation is consistently used throughout the entire series.
  • G-CO.6: This standard, using geometric descriptions for transformations, is addressed extensively. Examples of lessons addressing this standard are found in the Geometry materials on pages 24, 52 and 523.
  • G-GMD.4: This standard requires students to identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects. In Geometry, lessons 4.1, 4.4, 4.5 and 4.7 include rotations of rectangles, circles and triangles as well as the cross-sections of cylinders, spheres, cubes, pyramids and cones. Additionally, the lessons include applications of the volume formulas for cylinders and cones.

The following standards were identified as not being fully attended to in the instructional materials:

  • N-RN.1: The material provides an explanation of how the definition of the meaning of rational exponents follows from extending the properties of integer exponents but does not provide students the opportunity to explain themselves (Algebra 1 and Algebra 2).
  • N-Q.1: Units are attended to repetitively throughout the instructional materials, especially in Chapters 1 and 2 of Algebra 1, where this standard is addressed. However, the portion of this standard regarding interpreting the scale and the origin in graphs and data displays is not called out in the problems. The lessons begin with a table of values and then use that data to create a graph (sections 2.1, 2.2, 2.6). There were not student or teacher prompts that provided an opportunity for discussion, nor were there explanations or clarification about how the data in the table was used to create a scale for the graph.
  • N-Q.3: Determining level of accuracy is addressed on a basic level in the Algebra 1 materials in ways such as, "It isn't possible to have .3 boxes of popcorn so we must round up to the next box." Opportunities were not found that allowed students to consider the level of accuracy needed in ways such as, “Should we measure in feet or inches or sixteenths of inches?” or “Are integers or decimals two or three decimal places appropriate for the solution to a system?”
  • A-REI.11: This standard requires students to "explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately." This is addressed only for linear and quadratic equations. Polynomial, rational, absolute value, exponential, and logarithmic functions that are specified in the standard are not addressed in any of the instructional materials.
  • G-CO.2: The instructional materials provide students with the opportunity to represent transformations in the plane in a variety of ways. Students translate by moving the individual points of an angle (Geometry, page 52). Students also cut out the copy of a polygon and move it around the coordinate plane (Geometry, page 515). The materials do not address "describing transformations and functions." The materials have students analyze what happens to the x-values of the points of a figure and the y-value of points in a figure (Geometry, pages 517-518), but the materials do not have them write the transformation as a function.
  • G-CO.13: Inscribed equilateral triangle, square, and regular hexagon are not included.
  • G-GPE.5: Slope criteria is addressed in Geometry, lessons 3.1-3, but not as proofs.
  • G-CO.4: Several sections of materials throughout the Geometry materials focus on experimenting with transformations in the coordinate plane. Materials provide ample opportunities to translate, reflect, and rotate line segments and figures in sections 1.2, 1.4, 1.5, and 7.1 of Geometry. However, evidence was not found in which the definitions of rotations and reflections are developed in terms of angles, circles, perpendicular lines, and parallel lines as outlined in this standard.
  • S-ID.4: This standard requires students to: “use mean and standard deviation to fit it to a normal distribution and to estimate population percentages. Recognize there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve.” Problems were not found that included data sets where this procedure was not appropriate. There were no options for determining the area under the normal curve other than the text materials providing the percent for each interval.
  • S-IC.4 and S-IC.5: Evidence was not found of the use of simulation to attend to the standard.
  • S-CP.1: The instructional materials attend to the mathematical intent of the standard in that the terms, sample space and outcome, are consistently used throughout the probability sections of the materials. There is discussion of disjoint, intersecting, and complementary events (Geometry, sections 14.1, 14.2). However, there is no formal use of the term "union" used in the materials. Additionally, this standard is aligned to lessons beyond where the publisher shows in the alignment documents.

The following standards were identified as NOT ALIGNED to the mathematical content:

  • N-RN.3: This standard is not addressed, although Algebra 1, lesson 14.1 is related. There is a statement that operations of rational numbers is closed; however, no explanation is provided. Furthermore, there was no evidence regarding the operations of adding and multiplying of irrational numbers as closed operations.
  • G-MG.2: This standard was not identified in the publisher materials as being addressed in the materials nor was evidence of this standard found during the review process.

Additional notes about alignment:

  • G-CO.9: This standard requires students to prove theorems about lines and angles. There are lessons throughout Chapter 2 of Geometry about writing proofs, lessons about lines and angles, and tasks that allow students to develop their understanding and then write proofs. However, one concern about this particular standard is that the standard is aligned to lessons where the standard is not specifically addressed. For instance, Geometry, lessons 2.1 and 2.3 contains prerequisite skills in the lesson that lead up to the standard rather than addressing the actual standard that is aligned to a given lesson. These lessons are not actually aligned to any high school standards and are only aligned to G-CO.9 in the alignment guide provided by the publisher.

Indicator 1a.ii

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

Materials do not meet the expectation for attending to the full intent of the modeling process when applied to the modeling standards.

Each set of materials in the series includes a great number of lessons that contain a variety of components of the modeling process described in the CCSSM. However, these lessons are typically scaffolded to such an extent that students do not have an opportunity to work through the entire cycle of the modeling process independently. There are multiple applications, tasks and examples where restructuring the lesson to address the components of modeling would allow students to fully engage in the modeling process as required in the CCSSM. Students should have opportunities to be given a task/question/problem and then develop their own solution strategies, select the best tools for solving a problem or set of problems, create their own charts, graphs, and/or equations, evaluate and revise their and other answers, and report on their work - all for one task/question/problem rather than a part of the process for several different problems.

Examples of when and how components of the modeling process are attended to, and how they fall short, include:

  • Algebra 1 includes a blood alcohol content problem (section 16.4). Students are asked to compute, interpret, and report their work through a series of scaffolded steps. However, not all six steps of the modeling process are included. For instance, students do not choose a model to use – they are given a table to fill in and an equation to use to find the values.
  • In Algebra I, lesson 2.1: The Plane! Modeling Linear Situations, students model the height of a plane in flight. Students look at a number of models (graphs, tables, algebraic expressions) and interpret the models in terms of the context, but in every case, they are provided explicit support including partially completed tables and step-by-step directions.
  • Algebra 1 and Algebra 2 materials provide multiple opportunities to interpret features of graphs and tables (F-IF.4), yet lack all the steps included in the modeling process to meet the full intent of the modeling standard which this indicator requires.
  • In Geometry, Lesson 15.5, the problem is about the probability the dart will hit a shaded area (page 1212) and does provide students with an opportunity to formulate a solution path. However, the problem does not attend to other aspects of the modeling process. Students are not asked to validate their solution beyond "show your work;" they do not report their findings or revise their processes.

Notably, the “formulate” part of the modeling provided in the CCSSM is consistently lacking in the lessons provided in the materials. The CCSSM states that students should be “formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables." There was limited evidence that students were required to formulate a process for solving problems or work through the modeling process on their own.

Indicator 1b

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

Indicator 1b.i

The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.
2/2
+
-
Indicator Rating Details

The instructional materials meet the criterion of expectation that allow for students to spend the majority of their time on content from CCSSM widely applicable prerequisites. The scope-and-sequence provided shows a strong focus on the standards necessary for college majors, postsecondary programs and careers. Analysis showed this scope-and-sequence to be largely, though not entirely, accurate.

For example, Geometry, lesson 10.5 is aligned to G-CO.9, G-CO.12 and G-SRT.8 by the publisher.

Lesson 18 is “Exterior and Interior Angle Measurement Interactions: Sum of the Exterior Angles of a Polygon.” The components of the lesson have students writing formulas for the sum of the exterior angles of polygons, calculating the sum of the exterior angles of any polygon, writing formulas for the measure of each exterior angle of a regular polygon, calculating the measures of exterior angles and finding the number of sides given angle measures. Below is detail of how this lesson does/does not align to the standards the publisher’s content map indicated for the lesson.

  • G-CO.9: In Lesson 10.5, students use the theorems about lines and angles but the lesson is not designed to include proofs of either the theorems listed in the standard or other theorems. In fact, none of the learning goals for the section indicate that students will engage in proofs of any kind in this section.
  • G-CO.12: This standard is accurately aligned – students are making constructions in this lesson.
  • G.SRT.8: Students utilize trig ratios to solve one problem in the lesson. Trig ratios are not listed as a learning goal and are not an emphasis in the lesson.
  • G-CO.13: This standard DOES align to the lesson but is not mentioned at all by the publisher in either the Geometry text or alignment map for the course. This standard requires students to construct a square and a regular hexagon inscribed in a circle. Both of those constructions are in problem 3 of this lesson. The alignment document provided by the publisher aligns lesson 1.7 to this standard, but that is incorrect, too. The standard requires an equilateral triangle to be constructed and the triangle that is constructed in lesson 1.7 is not necessarily an equilateral triangle and therefore does not align to the standard.

Prerequisite material was mostly limited to “Warm-Up” tasks and used in a reasonable way to support meeting high school standards. Standards from Grades 6-8 are reviewed but not to an extent that is inappropriate. For example, Geometry, Chapter 14 begins by reviewing the middle school probability standards. A significant amount of time is not spent on this review, and it is an appropriate use of class time. After the first two review sections (approximately 135 minutes of class time according to the pacing guide), the other four lessons in the chapter transition to the high school probability standards. This was the only instance identified where more than just a portion of a lesson was spent on below grade-level standards, and the use of the review was appropriate in the context of the chapter and lessons.

The following examples show how the standards/clusters specified in the Publisher's Criteria for Widely Applicable Standards are developed in the materials.

  • The N-RN standards are included in both Algebra 1 and 2 materials; however, only three sections can be aligned to this strand of standards (Algebra 1 - 5.5 and 14.1, Algebra 2 - 9.4).
  • Many of the Algebra standards span throughout Algebra 1 and Algebra 2 materials in the series. Evidence for this is found in Chapters 1, 2, 3, 4, 5, 6, 7, 11, 12, 13 and 15 for Algebra 1; evidence is found in Chapters 1, 2, 3, 4, 5, 6, 7, 8, 9, 11 and 12 for Algebra 2.
  • F-IF standards span throughout Algebra 1 and Algebra 2 materials in the series. A variety of functions are interpreted and analyzed. Algebra 1 focuses on linear, quadratic, and exponential while Algebra 2 focuses on quadratic, polynomial, exponential, logarithmic, rational, and trigonometric. Both Algebra 1 and Algebra 2 have students graph functions and identify/analyze features of those functions.
  • S-ID.2 is in both Algebra 1 (throughout Chapter 8) and Algebra 2 (Section 15.1). Students build on their understanding of statistics from Grades 6-8 to compare the center and spread of a data set. Multiple representations are used: box-and-whisker plot, histogram, and stem-and-leaf plot.

The instructional materials do not include distracting content that is beyond than content expected to be taught in Algebra 1, Geometry, and Algebra 2.

Indicator 1b.ii

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

When used as designed, the instructional materials reviewed partially meet the expectation for allowing students to fully learn each standard.

The following are examples of where the instructional materials provide opportunities for students to fully learn non-plus standards.

A-SSE.1: The materials give students many opportunities to develop a deep understanding of these standards. Algebra 1 addresses these standards throughout with some specific examples in lessons 2.1, 2.2, 3.2, 3.4 and 5.1. Algebra 2 also continually makes reference to the components of expressions and equations and asks students to comment on the connection to the context of the problem.

The following are examples of where the instructional materials provide opportunities for students to partially learn non-plus standards.

A-CED.4: In Algebra 1, lesson 3.3, students re-write the temperature conversion formulas to solve for Celsius and Fahrenheit. This is the one example that was identified as addressing the aspect of the standard where students are required to rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI.1: The instructional materials provided insufficient opportunities for students to explain each step in solving a simple equation. Algebra 1, section 2.1 featured four examples in the textbook that required students to solve an equation and justify reasoning, although the "justifying" was overlooked as these steps were not included in the teacher edition. Justifications must be written out for a solved equation in Algebra 1, section 14.2. This section, however, is not aligned to this standard (it is aligned to N-RN.3), and the focus of this lesson is on the properties of real numbers rather than solving equations.

N-Q.1: Students have sufficient opportunities to interpret units and scale in the context of a variety of problems; however, the lessons always provide the units and scale. To fully meet the standard, students should be provided the opportunity to decide on units and scale.

N-RN.1: Algebra 1, Lesson 5.5 gives justification for properties of rational exponents but does not build to student explanations. The properties are shown with an example, and then students are expected to use them. These are not properties students are expected to know from prior grades, so the examples/explanations are not adequate and do not attend to developing conceptual understanding of the properties of rational exponents.

N-RN.2: Rewriting the radicals and rational exponents using the properties is included in Algebra 1, page 344; however, there are limited instances for student practice or development of the rules and few numbers without variables are included.

F-LE.3: Algebra 1, lesson 5.1, addresses this standard when comparing simple and compound interest. Algebra 2, lesson 5.4, also addresses this standard. However, the quantity and direct computations of problems in these lessons is not sufficient for mastery of this standard.

F-LE.4: The emphasis of the lessons aligned to this standard was on using the change of base formula. The components of the equation were not addressed, nor was base 2, which is specified in the standard.

A-SSE.3b: Algebra 1, lesson 2.7 primarily uses completing the square as a method to find zeros of a quadratic equation (ample opportunities for practice in textbook, skills practice, and assignment books). Two examples in the material (page 778) use completing the square to identify the vertex of a quadratic. The instructional materials do not use the language of maximum or minimum.

A-APR.6: No lessons ask students to use long division in the way specified by the standard -- that is, to recognize that division allows an equivalent form of the expression. The process of division is included, but the connection between the process and the zeros is not clear.

Indicator 1c

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

The instructional materials meet the expectation for being coherent and consistent with the high school standards that specify the mathematics which all students should study in order to be college- and career-ready. In addition, the materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The materials provide students with opportunities to engage in real-world problems throughout the courses. The students engage in problems that use number values that represent real-life values - fractions, decimals and integers. Solutions to problems also are typical of real-life situations. The context of most of the scenarios are relevant to high school students. Examples of where each book in the series meets the full depth are:

Algebra 1 - Analyzing representations of functions (sections 1.2, 1.3), rational functions (sections 7.5, 8.4), exponential and logarithmic functions (sections 10.2, 11.5), optimization (section 12.3).

Geometry - Diagonals in 3-D (section 4.8), similar triangles (sections 6.4, 6.6), trigonometric ratios (9.2-9.4), probability (Chapter 14).

Algebra 2 - Linear equations and inequalities (sections 2.3, 2.6, 3.2, 3.4), systems of equations and inequalities (chapter 6, 7), quadratic functions (section 11.1), piecewise and step functions (sections 15.1, 15.2), "modeling" type problems (Chapter 16).

Students are often asked to evaluate the work of others--very often from problems done by one of the "Crew" -- characters that are students who are presented at the beginning of the materials that are supposed to represent other high school students working on the lessons.

Students are given ample opportunities to engage with most non-plus standards through the textbook lessons, skills practice, and student assignment book. The skills practice focuses on practice of basic skills. Each section has a minimum of one worked-out example provided as a model that can be helpful for lower-performing students. The student assignment book focuses on applying skills to real-world scenarios and extending general knowledge to multi-step problems.

Indicator 1d

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

The materials meet the expectation for fostering coherence through meaningful connections in a single course and throughout the series. Both teacher and student materials provide opportunities to build new knowledge from current knowledge. Connections between and across multiple standards are made in meaningful ways.

The student and teacher materials often refer back to prior lessons to make connections and/or build understanding. Specific examples include:

  • Algebra 1, lesson 5.2 (page 417) refers to previously defined concepts such as regression equation and coefficient of determination, which were introduced in chapters 9, 13 and 16 of the same course.
  • Algebra 2, lesson 1.5 refers back to lesson 1.3 in the same course.

Student materials provide "Warm ups" at the beginning of each section that are primarily used to connect new learning to prior learning (Grades 6-8 or high school level). Specific examples are:

  • Algebra 1, lesson 11.4, uses the distributive property to introduce factoring (learned in Grades 6-8).
  • Geometry, lesson 11.1, introduces circles with a warm-up on drawing a circle with a given radius or diameter and then finding circumference and area (learned in Grades 6-8).
  • Algebra 2, lesson 2.1, identifies different forms of quadratic equations (learned in Algebra 1).

Learning goals are explicitly stated at beginning of each section ("In this lesson, you will…"); however, connections to prior learning are not explicitly made (i.e. "Previously you learned…).

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
1/2
+
-
Indicator Rating Details

The materials partially meet the expectation for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. Sometimes the material reviews some Grade 6-8 concepts, but not in a distracting or excessive way; rather, the material is presented in a manner that refreshes students and prepares them for the new concept.

Grades 6-8 standards are not clearly identified in teacher and student materials. However, there is a column labeled "Access Prior Knowledge" in the alignment documents that sometimes specified a middle school CCSSM to which the lesson is aligned. There are not very many explicit connections that link the lessons to prior learning for the teachers.

Examples of how lessons connect to middle school content include:

  • Students' exposure to calculating area and perimeter of two-dimensional shapes and calculating volume and surface area for three-dimensional shapes is built upon at the high school level through the use of application problems. The connection between two-dimensional figures and three-dimensional figures is a focus through the study of cross sections. Additionally, students learn how to calculate area and perimeter of a two-dimensional figure on a coordinate plane.
  • Cluster 7.RP: Ratios and proportional relationships is built upon at the high school level when learning about similarity of figures and related proportionality theorems (i.e., triangle proportionality theorem, proportional side theorem, proportional segments theorem, and triangle midsegment theorem).
  • The heading "Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers" under cluster 7.NS builds the foundation for the high school standard of A-APR.7 in which students rewrite rational expressions and perform operations with rational expressions.
  • N-RN.2 closely aligns with 8.EE.1 in the Grade 8 standards. Materials require students to apply exponent rules in Algebra 1 (section 5.5) and Algebra 2 (section 9.4), but this does not go beyond the expectations for the middle school standard.
  • 8.EE.8 ("Analyze and solve pairs of simultaneous linear equations") connects to standards A-REI.5, A-REI.6, A-REI.7, A-REI.11, and A-REI.12 in which students solve a linear equation algebraically and graphically and extend this to solving and graphing systems of linear inequalities.
  • In Grade 8, students learn how to utilize the Pythagorean theorem to determine unknown lengths of sides of right triangles and calculate distances in a coordinate plane. At the high school level, students are expected to prove the theorem and apply the Pythagorean theorem and its converse in the context of real world problems. Furthermore, the Pythagorean theorem serves as an introduction to 45-45-90 and 30-60-90 triangles.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.
0/0
+
-
Indicator Rating Details

The plus standards are usually identified in the supplementary alignment document as (+) standards. They are not identified as plus standards within the materials even though the standards are explicitly stated (teachers would need to know which standards are plus standards to know this within the lessons). Furthermore, plus standards are often within lessons that include non-plus standards. One concern is that the plus content cannot be separated from the non-plus standards within a lesson. Also, the plus standards are often in a lesson in the middle of a chapter (Algebra 2, lesson 7.4 contains at least two plus standards but lesson 7.5 does not). In order for students to accomplish the tasks in lesson 7.5, they must complete most problems in lesson 7.4. Therefore, a teacher could not choose to leave out plus standards and still complete all of the lessons not aligned to the plus standards.

Number and Quantity Standards: Three of eighteen plus standards for number and quantity are included in materials (N-CN.3, N-CN.8, N-CN.9)

Algebra Standards: Two of the four plus standards for Algebra are included in materials (A-APR.5, A-APR.7) Algebra 2, section 8.2 covers all operations with rational numbers to fully address standard A-APR.7.

Functions Standards: Eight of the eleven plus standards for functions are included in the materials (F.IF.7d, F-BF.1c, F-BF.4b, F-BF.4c, F-BF.4d, F-BF.5, F-TF.3, F-TF.7). F-IF.7a is thoroughly covered in sections 7.1-7.4 of the Algebra 2 textbook. Trigonometric plus standards add to work with trigonometric functions in non-plus standards and make connections to college course work.

Geometry Standards: Five of the six plus standards for Geometry are included in the Geometry textbook (G-GMD.2, G-SRT.9, G-SRT.10, G-SRT.11, G-C.4). Trigonometric plus standards do not deter from students' work with non-plus standards in defining trig ratios and using trig ratios to solve problems involving right triangles.

Statistics Standards: Four of nine plus standards for statistics are included in the instructional materials (S.CP.8, S.CP.9 , S.MD.6 and S.MD.7).

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed meet the expectation for rigor and balance. The aspects of rigor are balanced throughout the lessons, chapters and courses, and the lessons are often developed in a way to allow students to engage in relevant mathematics and develop their understanding. Many lessons begin with an application of the mathematical concept addressed in the lesson. Fluency is developed throughout the problems in the lessons and specifically through the work in the Student Skills Practice Book. The only concern is that many lessons are scaffolded in such a way that students are guided through a solution path or given properties to use that are not fully developed by the students. This step-by-step process diminishes the rigor of those lessons and inhibits the development of conceptual understanding.

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
1/2
+
-
Indicator Rating Details

The materials partially meet the expectation for supporting the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters. The lessons throughout the materials are generally well developed to allow students to build conceptual understanding of the key mathematical concepts. The few missed opportunities are noted below. The lessons, practice, and assessments allow for students to develop and demonstrate their understanding through a variety of methods including models, constructions, and application problems. The materials often provide students with opportunities to justify, explain and critique the reasoning of others; however, sometimes steps for solving problems are scaffolded in a way that restricts alternate ways of approaching a problem and therefore diminishes the cognitive demand of the lesson (see N-RN.1 below). Students are asked to demonstrate their understanding in a variety of ways including within class discussion, within groups and/or pairs, and individually. The materials generally provide some opportunities for students to build their understanding from simpler problems and numbers to more complex situations and numbers

The following are some specific ways the development of students' conceptual understanding is met:

F-IF.A: Function notation is consistently used and developed throughout the entire series. A sorting activity in Algebra 2, lesson 1.3 on pages 27-33 provides students with the opportunity to analyze relations (represented in an equation, table, graph, or scenario) and sort them into equivalent relations. As a follow-up, students are asked to determine which of the equivalent relations represents a function and which does not represent a function.

G-SRT.6: Geometry, lesson 9.1 features an exploration with ratios as an introduction to the trigonometric ratios of sine, cosine and tangent. Students are expected to calculate ratios of sides in given triangles (concrete) and generalize these findings to overarching questions near the conclusion of the exploration (i.e., "Is each ratio the same for any right triangle with a congruent reference angle? As a reference angle measure increases, what happens to each ratio?"). This concept is extended in section 9.2 on page 672.

S-ID.7: Students have many opportunities to develop their conceptual understanding of slope and intercept in the context of the data. The material repeatedly uses charts to break down functions into their components that the student must interpret in context and then draw conclusions about. Some examples of this are included in Algebra 1 on pages 170 and 176. Slope and y-intercept are again interpreted in context of a given scenario and data set in Algebra 1 on pages 524-525. Another example (page 531) is given in which the y-intercept must be obtained through extrapolation and the students must determine whether the extrapolated y-intercept makes sense in terms of the context.

Some specific places where opportunities for students to fully develop conceptual understanding are partially met:

N-RN.1 - The relationship between rational exponents and radical notation is provided to students in Algebra 1, sections 5.5 and 14.3, and in Algebra 2, sections 9.4 and 9.5. Although there are several opportunities with equivalent and simplified expressions, students are shown the rules and are expected to use them. For example, there are no connections for the product property between the exponent and repeated multiplication that would allow students to deepen their understanding of the properties rather than just repeat a rote process. A cut and paste grouping activity (Algebra 2, page 699) is utilized to group equivalent expressions that are written in non-simplified form. One question in this section (Algebra 2, page 707) shows three examples of student work and has the student determine whose work is correct. A similar question (Algebra 2, page 706) shows three different methods for simplifying an expression (all methods are correct; one uses radical notation while the other two use rational exponent notation), and students need to identify similarities and differences among the methods and explain in writing why all three are correct. Although the variety of activities are included, the activities only require students to apply rules that are given, not develop the rationale for those rules.

A-REI.A: This cluster is addressed in Algebra 1 Lesson 2.1, but not in a way such that students are required to justify the solution process. Students only have to solve problems and show work. The teacher notes suggest that the teacher ask about the process for solving and if there is more than one way, but the justification or construction of a viable argument is not required by the prompts provided. Additionally, this lesson includes these problems as a portion of the lesson but not the emphasis of the lesson; therefore, this standard is not fully developed in this lesson or in subsequent lessons in this course. In contrast, Algebra 2, Section 8.3 includes many opportunities to develop students' conceptual understanding of solving rational equations. A cut and paste sorting activity on page 631 is utilized to distinguish between the methods of cross-multiplying and using the least common denominator and when it is most advantageous to use each method. One question in this section (page 626) shows two examples of student work where each student uses a different method. Students are asked to compare and contrast the methods.

A-REI.11: This standard is thoroughly addressed only for linear and quadratic equations, and rational functions are addressed in only one example. Polynomial, absolute value, exponential and logarithmic functions that are specified in the standard are not addressed in any of the courses.

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The materials meet the expectation for providing many intentional opportunities for students to develop procedural skills and fluency. The lessons begin with a "Warm Up" problem that often review the procedure from a previous lesson or lessons. Within the lessons, students are provided with opportunities to develop procedures for solving problems that begin to develop fluency. The lessons provide students with a variety of practice experiences - some problems are completed with the whole class, others with partners and some independent. Each classroom lesson ends with a "Check for Students' Understanding" that is often furthering the development of procedural skills learned in the lesson. The materials also include a "Student Skills Practice" workbook and a "Student Assignments" workbook. Both of these workbooks continue to develop procedural fluency by providing significant opportunities for students to practice independently. The student skills practice that accompanies each course in the series primarily focuses on developing fluency of mathematical procedures.

Some highlights of strong development of procedural skills and fluency include:

A-APR.1 - Students are provided several opportunities to practice adding, subtracting, and multiplying polynomials within Algebra 1, Lessons 12.1 and 12.2 to enhance student fluency in conducting this skill.

A-SSE.2: The instructional materials provide multiple opportunities for building fluency with factoring (Algebra 1 Lessons 12.4, 12.5; Algebra 2, Lesson 4.2).

F-BF.3 - Materials strongly emphasize transformations of functions, and this is evident in the amount of practice the materials provide. For several types of functions (quadratic, radical, rational, exponential, logarithmic), students practice graphing a transformed function, write in words how f(x) is transformed to g(x), write transformed functions in terms of other graphed functions (example problems in Algebra 2, page 281 in the Student Skills Practice), and use a table to show how a reference point from a parent function is mapped to a new point as a result of a transformation.

G-GPE.4 - Materials provide several opportunities to use the distance formula and slope formula to classify quadrilaterals on the coordinate plane. All types of quadrilaterals are discussed in the materials.

G-GPE.5 - Materials provide several opportunities in Geometry, Section 1.5, to determine whether two lines are parallel or perpendicular given an equation or a graph with plotted points. Students also write an equation of a line passing through a given point that is parallel/perpendicular to a given line. Furthermore, in Geometry, Section 10.7 uses information about the slope of parallel and perpendicular lines to classify quadrilaterals on the coordinate plane.

Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The materials meet the expectation of the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. Students work with mathematical concepts within a real-world context. Sometimes contextual situations are used to introduce a concept at the beginning of a lesson while other times contextual situations are used as an extension of conceptual understanding. Single-step and multi-step contextual problems are used throughout all series materials and are intended to be utilized in different class settings (individual, small group, whole group).

Some standards/clusters that were particularly suited to application problems include N-Q.A, A-SSE.3, A-REI.11, F-IF.B, F-IF.7, F-BF.1 and G-SRT.8.

Additional considerations related to real-world applications:

  • When students are given a mathematical object within a provided context, the materials have students decompose the object into its individual terms in which students need to identify the appropriate unit, contextual meaning, and mathematical meaning. For an example, see the table on page 78 in Algebra 1.
  • Statistical concepts are taught within contextual settings requiring students to interpret data and make sense of their conclusions. For example, measures of central tendency are compared when analyzing the dot plots for the heights of players on two basketball teams. Polls and voting are used to provide context to teaching how to make inferences from population samples.

As noted previously, these applications are often given with extensive scaffolding, which could detract from the full depth of the standard being met, especially in regards to the modeling standards (see indicator 1aii).

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
2/2
+
-
Indicator Rating Details

The series materials meet the expectation of providing balance among conceptual understanding, procedural fluency, and application. No one aspect of rigor dominates problems/questions in textbook materials. In many lessons throughout the series, students are required to use multiple representations and written explanations to support their work and justify their thinking in order to demonstrate their understanding of procedures, skills, and concepts. The lessons generally provide opportunities for students to develop conceptual understanding - often through an initial application of a real-world concept - and are followed by opportunities for students to develop fluency through the "Student Skills Practice" sections.

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/8
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Criterion Rating Details

The instructional materials reviewed partially meet the expectation for connections between the MPs and the standards for mathematical content. The instructional materials do not provide specific information for aligning the MPs to the standards for mathematical content or to specific lessons. General information about the MPs is given at the beginning of each course within the teacher guides, but ongoing information for students or teachers is lacking. There are several components of the MPs within most lessons. However, teachers or students are not told which to focus on within the lessons because they are not specifically addressed/identified. An intentional structure for consistently addressing the MPs throughout the lessons would enhance the implementation of the MPs and benefit students and teachers.

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
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Indicator Rating Details

The materials partially meet the expectation of supporting the intentional development of overarching, mathematical practices (MP1 and MP6), in connection to the high school content standards, as required by the MPs. A very brief overview of the MPs and how they are generally addressed throughout the series is included at the beginning of each course textbook (for example, Geometry FM-22 to FM-30) as well as aligning the types of problems students will encounter to the MPs (for example, see Geometry FM-42 to FM-45). Although the material shows an example of each MP, no notation/justification is given for why or how that particular example relates to the identified MP.

For MP1, the introductory "supporting the practice" section in the teacher materials states that a key component is for students to make sense of problems and develop strategies for solving problems. Student development of strategies is not evident in the majority of lessons other than students creating a pathway to a solution that mimics the examples given or that follow a scaffolded process that is provided for students. These support structures reduce the level of sense making required to fully address this practice standard. If the scaffolded and/or repetitive structure was abandoned, students would have the opportunity to make their own sense of problems and develop their own methods for solving them.

MP6 is addressed throughout the materials. Students are often asked to use or create definitions, use units appropriately when necessary, and expected to communicate understanding clearly in writing and/or orally.

Although many of the components, of the practice standards are included in the lessons, the use of the practice standards would be enhanced if the publisher identified which practice standard(s) are best emphasized in each lesson or group of lessons to provide focus and direction to the teacher.

Indicator 2f

The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
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Indicator Rating Details

The materials partially meet the expectation of supporting the intentional development of reasoning and explaining, MP2 and MP3, in connection to the high school content standards, as required by the MPs.

For MP2, the overview says that this standard is addressed throughout the lessons because lessons often begin with real-world application and transition to mathematical representations. Although this may be a part of attending to MP2, this is not the entirety of the standard. For MP3, students often do construct viable arguments and do critique the reasoning of others. However, no additional support for helping teachers or students develop this standard is evident. It is stated that exemplar answers are provided but how to get students to get to those types of answers is not addressed. Some examples of how the materials align to components of MP2 and MP3 include:

  • "Thumbs Up" problems embedded throughout series materials provide opportunities for students to uncover a (potentially new) solution pathway and analyze the approach as they try to make sense of another student's work.
  • "Thumbs Down" problems embedded throughout series materials provide opportunities for students to analyze an incorrect solution pathway and explain the flaw in the reasoning that was provided.
  • "Who's Correct" problems embedded throughout the series provide opportunities for students to analyze several solution pathways and decide whether they make sense. If a solution pathway is incorrect, students are asked to explain the flaw in the reasoning that was provided.
  • In Algebra 1 and Algebra 2 materials, tables are utilized to consider the units involved in a problem (for example, Algebra 1 textbook, page 89). These tables provide the opportunity for students to attend to the meaning of quantities in an attempt to relate the contextual meaning and mathematical meaning of the provided scenario.

Problems frequently ask students to explain their reasoning. For example, Algebra 1 lesson 2.1 includes, “What is the slope of this graph? Explain how you know," but extensive use of scaffolding for problems reduces the depth of sense making required.

The material encourages students to decontextualize problems, often requiring them to come up with a verbal model or a picture of the problem and then put the mathematical measurements back in to find the answer. The material consistently provides opportunities for students to define the variables in the context of the problem and also define the terms of more complicated expressions within the context of the problem (Algebra 1, page 185).

The material consistently poses problems that require students to examine simulated student work, determine if they were correct or not, and defend their answers with solid mathematical reasoning.

Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
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Indicator Rating Details

The materials partially meet the expectation of supporting the intentional development of modeling and using tools, MP4 and MP5, in connection to the high school content standards, as required by the MPs.

For MP4, the information states that the materials provide opportunities for students to create and use multiple representations, and this is often true. However, there are not often specific instructions for teachers on how to make connections or get the connections from the discussion or even which connections to emphasize. For instance, in Algebra 1, lesson 11.6 on page 664, students have a table, a graph and a set of characteristics to identify. The guiding questions only call out characteristics of the problem and of using a calculator and do not make connections between the representations. The connections between the ways the zeros are represented is critical - in a table and on a graph. One question is "how do you use a graphing calculator to determine the x-intercepts?" This question gives no answers and has many - students can look at the graph, the table, or calculate it all using the calculator. No connections are made for teachers or students about why this is, and therefore, MP4 is lacking in this lesson.

Lessons throughout the series prompt students to engage in scaffolded steps in the modeling process as required by MP5.

  • A variety of tools are utilized to perform geometric constructions (i.e. compass, paper, pencil, rule, patty paper). Tools in the Algebra 1 and Algebra 2 materials are primarily limited to paper, pencil, calculator and/or graphing calculator. Students rarely have opportunities to choose an appropriate tool to use to solve a problem. Materials often includes, "Use your calculator to…" within directions. Many lessons demonstrate the steps of using a graphing calculator and then provide students with opportunities to use the results to help find solutions to problems (Algebra 1, pages 167 and 426).
  • Many lessons within the series utilizes multiple representations to model a problem context. For example, an exponential growth problem discussed in Algebra 1, pages 348-349, represents the scenario in a table, graph, and equation. Questions in the textbook are included to identify relationships among the representations.

Many lessons include mathematical models of real-world situations, but models are typically provided so that students are not asked to develop models themselves. For example, Algebra 1, lesson 2.1 includes a situation modeling the change in altitude of a plane but gives tables for students to complete and tells them to use one of the tables to draw a graph.

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
+
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Indicator Rating Details

The materials partially meet the expectation of supporting the intentional development of seeing structure and generalizing, MP7 and MP8, in connection to the high school content standards, as required by the MPs.

The materials require students to look for patterns, make generalizations, and explain the structure of expressions. Teacher-guided questions used during class discussions prompt students to look for structure and make generalizations. For example:

  • "How is the difference of two squares similar to the difference of two cubes? How is the difference of two squares different from the difference of two cubes" is asked during a lesson on factoring (Algebra 1 section 12.5).
  • "Why does this construction work?" is frequently asked of students in Chapter 1 of the Geometry textbook when students are making several constructions.
  • The teacher guiding questions included in Algebra 1, Lesson 1.2 are used to assist students in generalizing their findings after completing a sorting activity of graphs into a function group and a non-function group. Questions include: "Did all the graphs fit into one of the two groups? Can a graph be neither?" "What do graphs of non-functions look like?" "What do graphs of functions look like?" "Area all curved graphs considered graphs of non functions?" "Are all linear graphs considered graphs of functions?"

Some lessons include a focus on seeing structure and generalizing (e.g., Algebra 1, lesson 11.4 "Factored Form of a Quadratic Function"). Instructional materials frequently summarize a lesson by having students compare several problems and identify similarities as on page 219 of Algebra 1. However, most problems are typically scaffolded and provide students with a solution process which limits the students’ need to use structure and generalize. Students might be using repeated reasoning and structure to solve problems, but this is a byproduct of repeated practice or scaffolded examples rather than an intentional outcome of student discussion or problem-solving.

Gateway Three

Usability

Not Rated

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

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

Indicator 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ac.i

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

Indicator 3ac.ii

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

Indicator 3ad

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

Additional Publication Details

Report Published Date: 06/01/2016

Report Edition: 2013

Title ISBN Edition Publisher Year
978-1-60972-153-4
978-1-60972-154-1
978-1-60972-217-3
978-1-60972-218-0
978-1-60972-223-4
978-1-60972-224-1
978-1-60972-418-4
978-1-60972-638-6
978-1-60972-639-3
978-1-60972-640-9
978-1-60972-641-6
978-1-60972-642-3
978-1-60972-643-0
978-1-60972-644-7
978-1-60972-645-4
978-1-60972-646-1
978-1-60972-647-8
978-1-60972-648-5
978-1-60972-649-2
978-1-60972-652-2
978-1-60972-653-9
978-1-60972-654-6
978-1-60972-655-3

About Publishers Responses

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

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

Educator-Led Review Teams

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

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

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

Rubric Design

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

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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