Alignment: Overall Summary

The instructional materials reviewed for the HMH Traditional series do not meet expectations for alignment to the CCSSM for high school. The materials do not meet the expectations for focus and coherence as they partially meet the expectations in the following areas: attending to the full intent of the mathematical content contained in the high school standards for all students, allowing students to fully learn each standard, and making meaningful connections in a single course and throughout the series. 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 do not meet expectations for focus and coherence. The materials allow students to spend the majority of their time on the widely applicable prerequisites and attend to the full intent of much of the mathematical content contained in the high school standards for all students. However, the materials are lacking in the modeling process, and much work would need to be done in order to foster coherence.

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 instructional materials reviewed partially meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. In general, the series included the majority of all of the non-plus standards, but there were some instances where the full intent of the standard was not met.

Examples of how standards were fully met in the materials:

  • A-REI.6. Modules 11 and 12 in Algebra 1 include ample opportunities for students to solve linear systems exactly and approximately using various methods. In these modules, students solve systems of linear equations with numerous algebraic and graphical techniques as specified in the standard.
  • F-IF.A. The use of function notation and the underlying concepts as specified by the standards in this cluster can be found abundantly throughout the materials. Specifically, lessons 3.2, 3.3, 3.4, and 4.1 in Algebra 1 focus on domain, range, function notation, and recognizing sequences as functions that can be defined recursively. Moreover, the use of function notation as specified by these standards can be found throughout the Algebra 2 materials.
  • G-CO. The materials do an excellent job of attending to the entirety of all of the standards in this domain. Students are required throughout the Geometry coursework to experiment with transformations in the plane, understand congruence in terms of rigid motions, prove geometric theorems, and make geometric constructions. Notably, the materials thoroughly focus on congruency and similarity in terms of transformational geometry. For example, modules 2 and 3 in the Geometry coursework continually require students to use rigid transformations to look at congruency. Lesson 3.2 is appropriately titled “Proving Figures are Congruent Using Rigid Motions.”

The following standards were not fully met: N-RN.3, A-SSE.3, A-REI.2, A-REI.10, F-IF.9, and S-ID.4.

  • N-RN.3. In lesson 14.2 of the Algebra 1 materials, students will look at the properties of rational and irrational numbers. In this lesson, students will determine whether sums and products of numbers are rational or irrational as well as prove that rational numbers are closed under addition and multiplication. However, there was no evidence that students are required to explain that the product of a nonzero rational number and an irrational number is irrational.
  • A-SSE.3. Students factor and complete the square in order to rewrite quadratic expressions throughout the Algebra 1 and 2 materials (e.g., Algebra 1, lessons 20.2, 21.3, and 22.2; Algebra 2 lessons 3.1, 3.3 and 6.4). However, this standard requires students to “Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.” Evidence was not found that the materials require students to choose a form in order to reveal information. That is, students were directed to produce specific forms without opportunity for student choice. For example, Algebra 1, lesson 22.2, student exercises 17-18 (TE, page 1055) ask students to “rewrite the equation into vertex form, and solve the problem.”
  • A-REI.2. The materials require students to solve simple rational and radical equations in one variable, yet evidence was not found where students are required to give examples showing how extraneous solutions may arise. Algebra 2, lessons 9.3 and 11.3 work with rational and radical equations that give rise to extraneous solutions. Although students regularly check for extraneous solutions, evidence was not found to show students are required to explain how, why, and when extraneous solutions may arise.
  • A-REI.10. Lessons 6.1, 6.2, and 6.3 in Algebra 1 are noted by the publisher to address A-REI.10. However, no evidence was found that any of these lessons attend to A-REI.10. The Geometry and Algebra 2 materials do not specify any lessons dealing with A-REI.10, and evidence was not found that the materials address this standard. While looking for other potential occurrences, lesson 5.1 in Algebra 1 was found to require students to regularly “make a table, plot the points, and then connect the points.” However, students are not required to explain or indicate how they understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Students are asked in question #11 (TE, page 205) “What is a solution of a linear equation in two variables?” yet they are not required to explain how this relates to the entirety of the set of all solutions or how the solution relates to the graph of the equation.
  • F-IF.9. Lesson 6.5 in Algebra 1 requires students to compare the properties of two linear functions represented in different ways, yet evidence students were required to do this with other function types was not found. Notably, there was no evidence found that students are required to compare properties of two quadratic or two exponential functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • S-ID.4. Lessons 22.2, 23.2, and 23.3 in Algebra 2 require students to look at mean and standard deviation, determine when data sets appear to be normally distributed, calculate the percentage of data occurring within a given standard deviation from the mean, and estimate population percentages by using normal distribution curves. However, evidence was not found that students are required to recognize that there are data sets for which it is not appropriate to use a fitted normal distribution curve to estimate population percentages.

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 expectation for attending to the full intent of the modeling process when applied to the modeling standards. Although evidence for parts of the modeling cycle was found, the full cycle was rarely present. In particular, the materials routinely interrupt the modeling cycle. Each text in the series regularly directs the student to what variables are present, what assumptions to make, which model to use, and which conclusions to draw. Choices, assumptions, and approximations by students are rarely present throughout this series.

Two exemplar modeling tasks were found. The module performance tasks “How Big Is That Sinkhole?” (Geometry TE, page 976) and “How Much Does the Paint on a Space Shuttle Weigh?” (Geometry TE, page 1032) exemplify the modeling cycle. Students make assumptions, choose geometric representations, evaluate results, reconsider other assumptions in light of the situation, and report conclusions with supporting reasoning. Choices, assumptions, and approximations by students are present throughout these tasks.

However, nearly every lesson throughout the series fails to incorporate the full modeling cycle. Students are regularly given examples to follow and directed step-by-step. Examples of this include the following:

  • “The Canadian province of Saskatchewan has a shape that is almost exactly a regular geometric figure. That figure is an isosceles trapezoid” (Geometry TE, page 1072). Students are told what to assume and what geometric figure to use.
  • “Its territory can be modeled as a parallelogram” (Geometry TE, page 1049). Similarly, student choice and assumptions are not developed.
  • “Use this information to find a sine function that models this phenomenon” (Algebra 2 TE, page 938). Students are directed to the function type they should use in order to model the phenomenon. Student choice and assumptions are lacking. As a result, students need not consider the validity of the model being used or make adaptations to their model.
  • Lesson 20.3 in Geometry focuses on modeling. “Explain 2” on TE page 1060 looks at a tree canopy. In the example, the text states “Model the canopy with a hemisphere, and model the trunk with a cylinder whose height is three times its diameter.” When the lesson moves to “Your Turn” with a different tree situation, students are directed “Assume that the canopy can be modeled by a cone whose slant height is 4 times its radius, and that the trunk of the tree can be modeled by a cone whose height is 12 times its diameter. The formula for the lateral surface area of a cone is…” Students follow a prescribed sequence of steps as given in the examples as part of their "geometric modeling" rather than making their own assumptions, choosing their own model, and evaluating effectiveness of the model.
  • Lesson 12.3 in Algebra 2 specifies exercises 13-18 as modeling problems. Students are required to solve contextual problems like “How many [chess] matches were played?” These exercises require students to apply the formula for the sum of a finite geometric series to solve problems. However, multiple elements of the modeling cycle are missing in these problems. Students are given the important variables and the summation formula in order to perform operations/calculations. They are not required to interpret results, validate conclusions, consider revisions of the model, or report on the reasoning behind conclusions. Notably, students do not make assumptions in these exercises (e.g., “Assuming the pattern of new cases continues to follow a geometric sequences…” TE, page 625).

Although the lesson and module performance tasks were some of the best examples in these materials of attending to the modeling cycle, rarely did they fully incorporate the modeling cycle.

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 meet the expectation that, when used as designed, they allow students to spend the majority of their time on the widely applicable prerequisites (Publishers’ Criteria, table 1). As noted in indicator 1ai, the following standards were not fully met in the materials: N-RN.3, A-SSE.1, A-SSE.3, A-APR.3, A-REI.2, A-REI.10, F-IF.8, F-IF.9, and S-ID.4. Even as such, the materials allow students to spend the majority of their time on the content from CCSSM widely applicable prerequisites for a range of college majors, post-secondary programs, and careers.

In Algebra 1, students spend most of their time working with Widely Applicable Perquisites (WAPs) such as those from Number and Quantity, Algebra, and Functions. The Geometry course focuses daily attention on all the WAPs in the Geometry category. During Algebra 2, students will spend most of their time extending their understandings on Number and Quantity, Algebra, and Functions. Throughout all three courses, students will also spend time on the Statistics and Probability WAPs.

For example, in Algebra 1 students see sports connections to baseball (TE, page 943) while studying quadratic models (F-IF.7) and people diving into the water as part of their study on solving equations (A-REI.4). In Geometry, students consider roadways that people drive on (TE, page 695) in the study of trigonometric ratios (G-SRT.6). In Algebra 2, students examine car value depreciations (TE, page 658) during their work with exponential decay (F-BF.3) and work with compound interest (TE, page 696) in the study of exponential functions (F-LE.2).

Indicator 1b.ii

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

The materials partially meet the expectation for providing students with opportunities to work with all high school standards without distracting students with prerequisite or additional topics. The materials, when used as designed, allow students to fully learn most, but not all, standards.

The following are some examples of how the materials, when used as designed, would not allow students to fully learn each standard. (Those standards that were not attended to by the materials, as noted in indicator 1ai, are not mentioned here.)

  • N-RN.3. Lesson 14.2 of Algebra 1 requires students to determine if products and sums of numbers will result in rational and irrational numbers. Students also discuss whether the product of two rational numbers will yield an irrational number. Students also discuss closure of number systems under various operations. However, students rarely work with the product of a nonzero rational number and an irrational number.
  • A-SSE.1. Lesson 2.1 of the Algebra 1 materials provides opportunity for students to both identify and interpret components of expressions. Beyond this single lesson, however, the authors rarely call out further opportunities for students to interpret expressions in context. Later lessons in the Algebra 1 materials, including 14.2 and 17.1, are identified by the authors as supporting this standard, yet they do not provide opportunities for students to interpret structure in terms of a context. For example, section 14.2 of Algebra 1 has students rewriting radicals but does not attend to the full measure of the standard by interpreting structure in context.
  • G.CO.13. Students work on this standard only in lesson 6.1 in Geometry. Students are directed on how to construct these polygons in a circle, yet they are not given opportunities to practice.
  • A.APR.3. Lesson 20.2 in Algebra 1 requires students to graph a quadratic function and each of its linear factors in the four problems on TE, page 957. Throughout the Algebra 1 and 2 courses, students graph and factor polynomials. Students thoroughly practice finding zeros of polynomials, writing them in factored form and matching roots with factored forms of polynomials. In lesson 5.2 of Algebra 2, students are given factored forms of polynomials to sketch graphs by finding zeros. However, students are not required to factor polynomials in order to identify zeros and then create graphs.
  • F-IF.8.B. The only example found that would give support for F-IF.8.B alignment would be item 16 on TE, page 665 in the Algebra 2 materials where students are asked to “Use the properties of exponents to show why the function f(x) = 2^-x is an exponential decay function.” Typically though, students are not required to use the properties of exponents to interpret expressions for exponential functions. In contextual situations, students will be given formulas they are specified to use (e.g., example 3, TE, page 658, which states “Given the description of the decay terms, write the exponential function in the form f(t) = a(1 – r)t and graph it with a graphing calculator”) without any need to write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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 materials meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Throughout the series, students generally apply key takeaways from Grades 6-8 and engage in age-appropriate situations at a level of complexity suitable for students in this grade span. Lessons, though, regularly provide specific examples and directions for students to follow without allowing for true application of key work from middle school.

Examples of how key Grade 6-8 takeaways are applied:

  • The materials require students to apply ratios and proportional relationships with their work in Geometry, namely units 4 and 5 around similarity and trigonometry.
  • Students must apply concepts and skills of basic statistics and probability from 6.SP - 8.SP in their work with statistics throughout the series.
  • Exercises regularly require students to perform rational number arithmetic fluently in all the courses.
  • Throughout Algebra 1 and Algebra 2, students apply basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.

A survey of the materials reveals many examples where students are directed step-by-step to follow a procedure. For example, in Geometry lesson 7.1 (TE, page 315) students are told to "First, use the Polygon Angle Sum Theorem to find the sum of the interior angles..." Rather than "building on students’ previous knowledge and allowing students to make connections to new learning," the materials direct procedures. As such, the application of key Grade 6-8 takeaways could be strengthened.

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

Materials partially foster coherence through meaningful connections in a single course and throughout the series, where appropriate and where required by the standards.

Throughout the series, lessons within modules regularly build upon the work of previous lessons. For example, Algebra 1 module 17 progresses from the nomenclature of polynomials to adding and subtracting polynomials.

However, connections between and across multiple standards are rarely made in meaningful ways to support understanding of multiple standards at the same time. Modules typically contain 2-4 lessons with a sharp focus on specific standards or parts of standards. Rarely do the materials look at multiple standards at the same time in order to foster deep connections. Namely, the materials lack problems and activities that serve to connect two or more clusters in a domain, two or more domains in a category, or two or more categories, in cases where these connections are natural and important.

For example, module 14 in Algebra 1 looks at rational exponents and radicals. Although the next module focuses on geometric sequences and exponential functions, module 14 requires students to work on simplifying and evaluating expressions without making meaningful connections to standards outside of N-RN.A.

The Geometry standards are called out explicitly in only the Geometry materials. Nowhere in the Algebra 1 or Algebra 2 materials are there any explicit indications that students are working with Geometry standards. Similarly, the Geometry materials never explicitly call out any standards from the Number and Quantity, Algebra, or Functions conceptual categories. Even though connections are being made or could be made, the materials do not make the connections clear to teachers or students. Calling out the connections between standards to students and teachers would foster coherence throughout the series.

Additionally, Algebra 2 lessons 19.1-21.2 exactly duplicate Geometry lessons 21.1-23.2. These three modules, nine lessons in total, differ only in page and lesson numbers.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
0/2
+
-
Indicator Rating Details

The materials fail to explicitly identify and build on knowledge from Grades 6-8 to the high school standards. Neither the teacher or student editions mention standards from Grades 6-8, nor do the materials specifically call out connections from middle school content.

Throughout the series, the materials provide a "Tracking Your Learning Progression" section for each unit in the TE. Although these list student knowledge and understandings "Before," "In this Unit," and "After," nowhere in these sections are there any indications of middle school standards or work therein. Additionally, the "Math Background" notes in the TE were also void of explicit or implied connections to work from Grades 6-8.

For example, the teacher edition for Geometry begins Unit 1, "Transformations and Congruence," by noting that students, before the unit, should understand order of operations, using variables and expressions to represent situations, locating points in a coordinate plane, and solving equations. However, nowhere in the teacher or student materials are any connections called out around the major work of Grade 8 on congruency and transformations.

Furthermore, the materials presume no previous student knowledge when introducing similarity. Unit 4 of Geometry begins by defining dilations, similarity transformations, etc., without any mention of the work students do in Grade 8 with similarity.

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

Of the 43 plus standards and 5 plus substandards included in the CCSSM, the materials work with 10 of them: N-CN.8, N-CN.9; A-APR.7, G-SRT.9, G-SRT.10, G-SRT.11; S-CP.8, S-CP.9, S-MD.6, and S-MD.7. The materials attend to the fullness required by these standards with the exception of N-CN.8. In general, the materials treat these 10 standards as additional content that extend or enrich topics within the unit and do not interrupt the flow of the course.

Some examples:

Algebra 2, lesson 7.2 stands alone as a lesson where students can know the fundamental theorem of algebra and see how it applies to polynomials, not only quadratics. The lesson does a thorough job attending to N-CN.9. This lesson connects with the work of the unit and could be used or omitted in the classroom without compromising the flow of the course.

Lessons 9.1 and 9.2 in Algebra 2 focus mainly on the mechanics of adding, subtracting, multiplying, and dividing rational expressions. Lesson 9.2 has components, like “Explain 3”, that turn students’ attention to the conceptual understanding required by A-APR.7. As such, the incorporation of A-APR.7 strengthens the lessons. With the treatment of A-APR.7 as presented, teachers have the liberty to include or exclude A-APR.7 without interrupting the course progression.

As part of Lesson 13.4 in Geometry, students will see a derivation of the formula A = ½ ab sin(C) for the area of a triangle (G-SRT.9), yet they are not required to derive the formula themselves. The emphasis of the lesson revolves around “solving right triangles,” and, as such, student understanding is deepened with the addition of G-SRT.9 if teachers choose to include it.

Lesson 22.3 of Geometry, “Dependent Events,” appropriately follows after “Independent Events” of Lesson 22.2. Students work extensively with S-CP.8 in this lesson. (See also lessons 20.1-2 of Algebra 2, as they are exact copies of these lessons.)

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: 06/01/2016

Report Edition: 2015

Title ISBN Edition Publisher Year
9780544381896
9780544381964
9780544385818
9780544385825
9780544385917
9780544385924

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The publisher has not submitted a response.

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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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