Alignment: Overall Summary

The instructional materials reviewed for the Big Ideas Integrated series do not meet expectations for alignment to the CCSSM for high school. The materials do meet the expectations for allowing students to spend the majority of their time on the content from the CCSSM widely applicable as prerequisites, but they do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. The materials partially meet the expectations for the remainder of the indicators within Gateway 1, and since the materials did not meet the expectations for focus and coherence, evidence for rigor and the mathematical practices in Gateway 2 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Does Not Meet Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
9/18
+
-
Criterion Rating Details

The instructional materials reviewed for Big Ideas Integrated do not meet the expectation for Focus and Coherence within the CCSSM. For focus, even though students have the opportunity to spend the majority of time on the WAPs, students do not have the opportunity to fully learn all aspects of the non-plus standards. The contexts of problems are appropriate for high school students, but the numbers used in the exercises are often integers or lead to integer solutions. Also, the full intent of the modeling process is not applied to the modeling standards. For coherence, there are partial connections within and between courses, and explicit and purposeful connections to the standards from Grades 6-8 are also partially present.

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 meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Although most non-plus standards were addressed, multiple standards were only partially addressed.

For some standards, the materials only addressed certain aspects of the standard. For example:

  • N-Q.1,2: Throughout the series, students are always provided the units to use in their problems. When contexts are used, students are given the appropriate units, and in most problems, they are given the units to use in their solution process. Examples of this include:
    • In exercises involving area and volume, the unit of measure is consistent so that the student does not have to choose to convert units and decide which unit of measure to use for reporting solutions.
    • In other real-life problems, units could be used to gain understanding, as in problem 38 of Lesson 1.5 or problem 22 in Lesson 3.3 (both in Integrated Mathematics I), but students are not given opportunities to use units to solve problems that would require a series of conversions.
  • For G-CO.3, the materials do not address the reflection of an object onto itself. In Integrated Mathematics I, 11.2, the materials ask students about lines of symmetry but do not ask students to describe reflections that carry a polygon onto itself. Lesson 11.3 does ask students to describe rotations that map a figure onto itself in problem 20 and to select angles of rotation symmetry for a given regular polygon in problems 21-24, which addresses the portion of the standard concerning rotations.
  • S-IC.4 requires students to develop a margin of error through the use of simulation models for random sampling. In Integrated Mathematics III, Lesson 10.5, students calculate a sample mean and sample proportion and use those to estimate the population parameters. Students learn a formula for calculating a margin of error but do not “develop a margin of error through the use of simulation models for random sampling.”
  • S-IC.5: In Integrated Mathematics III, Lesson 10.6, problems 3-4 and 7-9 do "use data from a randomized experiment to compare two treatments," and although problems 7-9 have students use simulations to calculate the differences between the means of two groups and draw a conclusion, the conclusion that is drawn does not include whether or not the differences are significant.
  • For S-CP.5, students are given the formula for conditional probability, and then they are directed to use and apply the formula. When asked to explain the concept of conditional probability, they are asked to explain in terms of dependence and not independence. Students are not prompted to explain or make the connection between conditional probability and independence.

Indicator 1a.ii

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

The materials do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. Many of the modeling standards have not been completely addressed with the full intent of the modeling process by the instructional materials of the series, and some aspects of the modeling process are missing within the materials.

According to the CCSSM, modeling has attributes such as choice, decision-making, creativity, estimation, drawing and validating conclusions, design and re-design, as well as reasoning and communicating. Scaffolding within the lessons, practice problems, extension resources, and the performance assessment tasks prevents students from engaging in the full modeling process, and opportunities for students to engage in validation, reporting of conclusions, and the reasoning behind them were routinely omitted from problems. Also, there were many problems in the materials labeled as Modeling with Mathematics that attended to either MP4 or were application problems because they were missing at least one part of the modeling process. Examples of incomplete opportunities to engage in the full modeling process include hte following:

  • In Integrated Mathematics I, the exploration for Section 6.6 focuses on a context of rabbits reproducing. Students determine the number of pairs of rabbits after a given number of months. The reproduction pattern is described, and the exploration states that the numerical pattern is exponential and gives a picture. Numbers are organized in a table with places for students to finish by filling in blank spaces. This guides the student solution strategy and inhibits the modeling process from unfolding.
  • In the student resources for Integrated Mathematics I, the enrichment and extension exercise for 3.1 gives a quadratic rule in the context of jumping off a diving board. Within this exercise in relation to F-IF.4, students are given the opportunity to interpret key features of graphs and tables in terms of the context. However, rather than asking students to model, analyze and interpret the function, the problem specifically tells them how and what to interpret. Students are instructed to graph the function with t on the horizontal axis and construct a table with time increments of tenths of a second. These specifications take away the first part of the modeling process in which students identify variables in the situation and select those that represent essential features. There is also no request for the final part of the modeling process in which students report their conclusions and the reasoning behind them.
  • In Integrated Mathematics II, the performance task for Chapter 2, "Flight Path of a Bird," includes scaffolding that prevents the full modeling process from taking place. A quadratic model is given, and then students are guided to write an equation, graph it, interpret the graph and answer questions about the model using the graph. Student decisions about how to analyze and interpret the quadratic model for the bird path is overly guided by instructions, diagrams, and guidance about solution strategies and the completion of calculations.
  • In Integrated Mathematics II Lesson 9.1, problems 13 and 14 use the Pythagorean theorem to solve a right triangle application problem, but students are not engaged in the entire modeling process. The questions are prescriptive as they refer to an example to follow, and students are told to use the Pythagorean theorem. The right angle is drawn and labeled for the students.
  • In Integrated Mathematics II Lesson 3.7, problems 19, 20 and 30 have the variables already defined, and students are told which variable is independent. Students are asked to determine if the given data is linear, exponential, or quadratic and to explain their reason, but there is no opportunity to define variables, interpret results in context or consider the need for reevaluation.
  • In Integrated Mathematics III, the Performance Task for Chapter 1, entitled Population Density, gives students the opportunity to formulate a model/plan for attendance boundaries given a list of constraints, and then students can compute and interpret their results based on the formation of the problem. This task does not, however, indicate how students would be expected to validate their results and, then, either report those results or complete any re-formulations that might be needed.

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 materials, when used as designed, meet the expectations for allowing students to spend the majority of their time on the content from the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers. The Widely Applicable Prerequisite Standards (WAPs) are a focus across the series.

  • In Integrated Mathematics I, the first half of the course (Chapters 1-6) is focused on the WAPs from Algebra and Functions. The Algebra WAPs continue to be supported through integration with geometric concepts in Chapters 8, 9, 10, and 12.
  • Chapters 1-4 of Integrated Mathematics II are focused on WAPs as students work with a broader range of equations and functions. Chapters 6-9 focus on WAPs through geometric investigations of triangle relationships, polygons, similarity and right triangle trigonometry.
  • The only chapters within Integrated Mathematics III that do not have a heavy focus on the WAPs are 1, 9, and 10. Chapter 1 focuses on G-MG.1-3 and G-GMD.4, and Chapters 9 and 10 address trigonometric identities and formulas, data analysis, and statistics. Otherwise, Integrated Mathematics III is focused on the WAPs throughout Chapters 2-8.

This relatively balanced distribution of WAPs across all three courses of the Big Ideas Integrated series for high school is a strength of the materials.

Indicator 1b.ii

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

The instructional materials reviewed for Big Ideas Integrated Series partially meet the expectations that the materials, when used as designed, provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics. The materials for the series, when used as designed, would not enable students to fully learn some of the non-plus standards.

There were a number of examples where the materials would not enable students to fully learn a particular standard. Specific examples are shown below:

  • G-CO.1: This standard asks students to know geometric definitions based on "undefined notions of point, line, distance along a line, and distance around a circular arc." Across the series, this standard was addressed by telling students there are undefined notions in geometry (with the exception of distance around a circular arc), and the geometric definitions were not developed based on the undefined notions.
  • N-RN.3: The standard asks students to "explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational." In Algebra 1, Lesson 4.1, problem 99 has students perform a limited number of calculations with pre-selected numbers, and then, students use that information in problem 100 to answer if this is always, sometimes, or never true. These are the two problems that offer opportunities to address N-RN.3.
  • Additionally, it is important to note that there were a number of standards, for example, A-REI.5 (Integrated Mathematics I, 5.3), G-SRT.7 (Integrated Mathematics II, 9.5) and S-ID.5 (Integrated Mathematics I, 7.5), which were addressed in one lesson throughout the series.

For standards that require students to derive, prove or explain, the materials often provide a derivation, proof or explanation rather than providing students with the opportunity to show their own understanding. Examples are shown below:

  • N-RN.1 requires students to explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponent to those values. In Integrated Mathematics II, Lesson 1.5, an explanation was provided to students, with no opportunity for student explanations.
  • G-C.5 calls for students to derive the fact that the length of the arc intercepted by an angle is proportional to the radius. In Integrated Mathematics II, Lessons 11.1-11.2, the derivation of arc length and the formula for area of sectors is provided for students. Students are not required to engage in constructing a derivation.
  • G-GPE.2 requires students to derive the equation of a parabola given a focus and directrix. In Integrated Mathematics II, Lesson 3.6, the derivation is given to students, with no opportunity for active engagement or input by the student.

For some standards, the materials do provide sufficient opportunities for students to fully learn the standards. Examples where the materials provide sufficient opportunities for students to fully learn a standard include the following:

  • F-IF.2: The materials introduce function notation to students in Integrated Mathematics I during Lesson 3.3, providing a description of function notation and how to use it to evaluate functions for specific input values and practice in using function notation when solving familiar problems in mathematical contexts and real-world contexts. Skill in utilizing function notation is continually promoted throughout the remainder of the series with the regularity of using function notation increasing from Integrated Mathematics I through Integrated Mathematics III. For example, by the end of Integrated Mathematics I, students build fluency in seeing f(4) = -2 as (4, -2) . In Integrated Mathematics II and III, basic skills extend to more complex uses of function notation, such as seeing Δy/Δx as or describing function transformations using f(x) notation.
  • F-BF.3: In Integrated Mathematics I, students develop understanding of transformations with linear and exponential functions. In Integrated Mathematics II, students begin working with absolute value and quadratic function transformations. In section 3.4 of this course, students learn how to identify even and odd functions. There is a specific example to address identifying even and odd functions from the rules, and there is a study tip to expose students to identifying even and odd functions from a graph. There are practice problems to address both. Students continue to practice and develop understanding of transformations of functions in Integrated Mathematics III. In earlier chapters of this course, students work with transformations on function types previously learned in the first two courses. Students then develop understanding of transformations with new functions (polynomials, radical, exponential and logarithm, rational, and trigonometric) as they learn them.

Indicator 1c

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

The instructional materials reviewed partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials regularly use age-appropriate contexts and apply key takeaways from Grades 6-8, yet do not vary the types of real numbers being used.

Throughout the series, many examples, exercises, and problems include real numbers that, in many instances, provide limited opportunities for students to use decimal and fractional constants, coefficients and solutions.

  • In Integrated Mathematics I, the chapters that address linear equations, linear inequalities and geometric concepts avoid fractions, decimals and irrational numbers. Chapter 1 focuses on solving linear equations, and in Lesson 1.1, students solve one-step equations in examples and practice problems that use values integer coefficients, numbers that divide or multiply easily to give integer results, or fractions that have the same denominator.
  • In Chapter 11 of Integrated Mathematics II, the figures in the exercises addressing area, surface area, and volume typically have dimensions that are whole numbers. When calculating area, surface area, or volume, the solutions are typically whole numbers unless the figure involves a circle or finding the area of a regular polygon. In those exercises where a missing dimension needs to be found, the solution is typically a whole number except for figures that involve a circle or finding the area of a regular polygon.
  • In Lesson 6.5 of Integrated Mathematics III, students solve rational equations, and for most of the equations, the solutions are integers or simple rational numbers. This also occurs when students solve radical equation and inequalities in Lesson 4.4 and exponential and logarithmic equations in lesson 5.5.

Contexts include a variety of topics that help engage learners with different interests at a level appropriate to high school. Contexts include, but are not limited to: sports, animals, income, profit, investments, driving cars, and population density. Opportunities for experience with key take-aways from Grades 6-8 were prevalent, with the following seen more strongly than others:

  • Applying ratios and proportional relationships
  • Applying basic function concepts; e.g., by interpreting the features of a graph in the context of an applied problem
  • Applying concepts and skills of geometric measurement; e.g., when analyzing a diagram or schematic
  • Applying concepts and skills of basic statistics and probability (see 6-8.SP)

There were limited opportunities to apply the following key-takeaways:

  • Performing rational number arithmetic fluently
  • Applying percentages and unit conversions; e.g., in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3, acre-feet, etc.)

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for fostering coherence through meaningful mathematical connections in a single course and throughout the series, where appropriate and where required by the Standards. While there is some evidence of mathematical connections within courses and across the series, overall the connections among standards within and between courses are not clearly shown for teachers. Even when solid connections exist within the mathematics, those connections may not be utilized to enhance the students' learning and understanding of the mathematics.

Some of the lessons and chapters are not connected to other lessons and chapters within the course/series where connections would be appropriate. For example:

  • In Integrated Mathematics I, Chapter 7 primarily addresses analyzing and displaying univariate data, but there are no connections made to the analysis and display of bivariate data presented in lessons 4.4 and 4.5 of the same course. There was also no indication for teachers as to if or how the content of Chapter 7 would connect to future courses in the series.
  • In Integrated Mathematics II, there is no connection made between geometric probability addressed in Lesson 11.2 and Chapter 5, Probability.
  • In Integrated Mathematics III, the summary for Chapter 1, Geometric Modeling, indicates general concepts from the first two courses in the series that students will use in the chapter, but there are no other direct references to either Chapter 11, Circumference, Area, and Volume, of Integrated Mathematics II or Lesson 8.4, Perimeter and Area in the Coordinate Plane, of the first course.
  • In Integrated Mathematics III, the summary for Chapter 10, Data Analysis and Statistics, indicates general concepts from the first two courses in the series that students will use in the chapter, but there are no other direct references to either Chapter 5, Probability, of Integrated Mathematics II or Chapter 7, Data Analysis and Displays, of Integrated Mathematics I.

The following examples include characteristics of the instructional materials reviewed that may promote mathematical connections within and between courses but do not clearly articulate those connections.

  • The Teacher Edition includes overviews of the sections in each chapter as well as a chapter summary. Both the overviews and the chapter summaries indicate general concepts and skills teachers can expect their students to know from middle school and/or previous courses, but neither of these sections provide direct connections to previous courses.
  • The student materials occasionally include “remember” arrows (as on pages 254 and 255 of Integrated Mathematics II) or phrases like “Previously, you…” that contain information about a previously learned concept. For example, in Lesson 2.6 of Integrated Mathematics III, the materials state, "Previously, you used transformations to graph quadratic functions in vertex form. You can also use the axis of symmetry and the vertex to graph quadratic functions written in vertex form". However, these aids do not foster direct connections within and among courses of the series.
  • The connections between standards are listed in the Correlation to the Common Core State Standards Table of Contents documents for each course. However, the connections are not explained or emphasized for the teachers. These documents are not included in the Teacher Editions.
  • There are "Connections to Algebra" and "Connections to Geometry" symbols and notes included in the lesson examples that make students and teachers aware that this is a concept that can be connected to other concepts in the course or series; however, these are used only occasionally. Some of these connections are very specific, as on page 390 of Integrated Mathematics I that states "In this step, you are applying the Substitution Property of Equality that you learned about in Section 1.1." Others are general or vague, as on page 405 of Integrated Mathematics I, where it states, "In this exploration, you expand your work on perimeter and area into the coordinate plane".

The following are examples within the series materials that do promote and foster coherence:

  • At the beginning of each chapter across the series, there is a "Maintaining Mathematical Proficiency" activity that reviews important concepts and skills from previous grades or courses. These activities help students connect prior learning to new learning in the chapter they are beginning.
  • Students work with area, surface area, and volume in middle school, and these geometric concepts are reviewed in the last chapter of Integrated Mathematics II. The chapter extends this review work to include the area of regular polygons and surface area and volume of a variety of 3D figures not included in the middle school standards.
  • In Integrated Mathematics I, students develop linear and exponential equations and functions. Then in Integrated Mathematics II, they extend their algebraic reasoning and understanding of functions with quadratic, absolute value, and polynomial functions. Finally, in Integrated Mathematics III, students study polynomials, radicals, logarithmic, rational, and trigonometric functions. In each of the three courses, students' ability to interpret the structure (A-SSE), perform arithmetic (A-APR), create equations (A-CED), reason with equations and inequalities (A-REI), and interpret functions (F-IF) builds upon the previous course. Students are given the opportunities to augment their work with many function types in these domains across the series.

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 expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. Overall, content from Grades 6-8 is present but is not explicitly identified and does not always fully support the progressions of the high school standards. There is some support for making connections between standards from Grades 6-8 and high school as seen in Laurie's Notes and Maintaining Mathematical Proficiency.

The following are examples of where the materials do not explicitly identify and/or build on standards from Grades 6-8:

  • The Chapter Summary pages for all courses have a What Your Students Have Learned…Will Learn section, and throughout the series, this section includes references to topics or concepts students learned in middle school. However, when referencing these concepts from Grades 6-8, specific standards are not explicitly identified, and there are not clear connections between standards from Grades 6-8 and high school.
  • Lessons 1.1-1.3 and 2.1-2.4 of Integrated Mathematics I are identified in the CCSSM document as addressing A-CED.1 and A-REI.3. These lessons address solving linear equations and inequalities, which aligns to standards from 8.EE.C, but there are no standards identified from Grades 6-8.
  • Lessons 5.1-5.4 of Integrated Mathematics I address solving systems of linear equations graphically and symbolically for systems having one solution, no solutions and infinitely many solutions, which aligns to standards from 8.EE.C. The teacher materials do indicate that the concepts are being repeated from Grades 6-8, but no specific standards are identified. Also, the teacher materials do provide some pacing suggestions for these lessons, but there is no guidance for how to build on these concepts in order to enhance the learning for high school students.
  • The Chapter 7 Summary of Integrated Mathematics I indicates the construction and interpretation of box-and-whisker plots as new learning rather than prior learning from middle school, but the overview for Lesson 7.2 states that “students should be familiar with representing data using box-and-whisker plots from middle school.” There are no standards from Grades 6-8 identified.
  • Chapter 11 of Integrated Mathematics II mainly addresses area, volume, and surface area, which are concepts that have their origins in standards from Grades 6-8. However, there are no standards from Grades 6-8 identified, and the connections between the high school concepts and the concepts for Grades 6-8 are only described in the teacher materials.

The Maintaining Mathematical Proficiency lessons at the beginning of each chapter connect to concepts from Grades 6-8 as this section reviews concepts or skills that will be needed throughout the chapter. Most of the work with middle school concepts or skills in these lessons is intended to reinforce course-level standards, but identification of the concepts or skills from Grades 6-8 is inconsistent. For example, in Chapter 1 of Integrated Mathematics 1, adding, subtracting, multiplying, and dividing integers is specifically noted as Grade 7 work, but in Chapter 2 of the same course, graphing numbers on a number line and comparing real numbers are not identified as work from a previous grade.

An example of the materials attending to the progressions of standards that are referenced in the progression documents is in Chapter 11 of Integrated Mathematics 1. The publisher describes concepts from middle school that relate to what students will be learning, and the middle school concepts include the types of transformations students are familiar with and their understanding of congruency. In the introduction to Lesson 11.4, teachers are told, "In Grade 8, the concept of congruency was introduced. Students should understand that a two-dimensional figure is congruent to another when the second can be obtained from the first by a sequence of rotations reflections and translations." In Lesson 11.4, the understanding of congruency through rigid motions is continued, and then, students develop triangle congruency theorems through rigid motions in Chapter 12.

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, when included, are not explicitly identified in the teacher or student editions of the materials. The correlation charts of lessons-to-standards and standards-to-lessons found in the front matter of the Teacher Editions do not denote which standards are plus standards. Alignment of plus standards was in a separate set of course alignment documents titled, Correlation to the CCSSM (I, II, and III) Table of Contents.

The plus standards that are included in the materials typically support the mathematics which all students should study in order to be college- and career-ready in a coherent manner, and the plus standards typically could be omitted without interfering with the flow of the content within the series.

In Integrated Mathematics II, the following plus standards are addressed in the given lessons: S-CP.8 (Lesson 5.2); S-CP.9 (Lesson 5.5); G-C.4 (Lesson 10.1); and G-GMD.2 (Lessons 11.4 and 11.7). In Integrated Mathematics III, the following plus standards are addressed in the given lessons: A-APR.5 (Lesson 3.2); N-CN.8,9 (Lesson 3.6); A-APR.7 (Lessons 6.3 and 6.4); F-TF.9 (Lesson 9.2); G-SRT.9-11 (Lessons 9.3 and 9.4); and S-MD.6,7 (Lessons 10.2 and 10.5).

Some lessons do not reach the full intent of the plus standards.

  • In Integrated Mathematics III, Lesson 3.6 does not give students the opportunity to show that the Fundamental Theorem of Algebra is true for all quadratic polynomials, which is an aspect of N-CN.9, but it does give students the opportunity to fully address N-CN.8.
  • In Integrated Mathematics III, Lessons 6.3 and 6.4 do not give students the opportunity to "understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression", which is an aspect of A-APR.7.
  • In Integrated Mathematics III, Lesson 9.2 does not give students the opportunity to prove the addition and subtraction formulas for the tangent ratio, which is part of F-TF.9.

Gateway Two

Rigor & Mathematical Practices

Not Rated

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

Criterion 2a - 2d

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

Indicator 2a

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

Indicator 2b

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

Indicator 2c

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

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
N/A

Criterion 2e - 2h

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

Indicator 2e

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

Indicator 2f

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

Indicator 2g

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

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Gateway Three

Usability

Not Rated

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

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

Indicator 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ac.i

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

Indicator 3ac.ii

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

Indicator 3ad

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

Additional Publication Details

Report Published Date: 10/18/2016

Report Edition: 2016

Title ISBN Edition Publisher Year
978-1-68033-051-9
978-1-68033-052-6
978-1-68033-054-0
978-1-68033-055-7
978-1-68033-068-7
978-1-68033-070-0
978-1-68033-071-7
978-1-68033-073-1
978-1-68033-074-8
978-1-68033-087-8
978-1-68033-089-2
978-1-68033-090-8
978-1-68033-092-2
978-1-68033-093-9
978-1-68033-112-7

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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