Alignment to College and Career Ready Standards: Overall Summary

Course 3 minimally addresses major coursework of the Grade 8, and future grade level work is taught and assessed. Chapter 3 covers work with graphs and functions. Chapter 4 works with exponents and roots is completely aligned with Grade 8 standards.  Chapter 11 has work that covers multi-step equations and inequalities. Chapter 12 covers major coursework on graphing but also contains standards that are above Grade 8.

 Much of this material focuses on standards below Grade 8. Since these materials do not meet the expectation for alignment to the CCSSM in focus or coherence, they were not reviewed for rigor and the mathematics practices.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
0
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
0
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 8 do not meet the expectations for Gateway 1. While there are lessons in which the supporting work enhances the understanding of the major work of Grade 8, approximately 12% of time is dedicated to major work for Grade 8. This number was found by dividing the number of instructional days dedicated to major work (22 days) by the total number of days to complete the entire course (180 days). Too many assessment questions were on standards from above Grade 8.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
0/2
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for assessing materials at the Grade 8 level. There were many assessment items aligned to standards above Grade 8 in this course. Some examples of these high school standards are A.REI.D.12 and A.APR.A.1.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
0/2
+
-
Indicator Rating Details

The instructional materials for Grade 8 do not meet the expectations for assessing materials at the Grade 8 level. Overall, there are too many items that align most closely to standards above Grade 8 whose inclusion is not mathematically reasonable and whose alteration or omission would significantly impact the underlying structure of the materials.

  • In Chapter 12, there are assessment items involving linear inequalities in two variables, which most closely aligns to A.REI.D.12. Although this is only a slight extension of the Grade 8 standards involving linear equations in two variables, this inclusion introduces confusion for students as they are initially creating and manipulating equations in two variables. This confusion makes the inclusion of inequalities in two variables mathematically unreasonable.
  • In Chapter 13, there are assessment items involving arithmetic and geometric sequences, which align most closely to standards from F.LE. There are also assessment items involving quadratic and exponential functions, which align most closely to standards from F.IF. The inclusion of these topics is not mathematically reasonable as they expect students to identify discrete and specific non-linear situations when Grade 8 grade standards expect students to identify linear or non-linear situations in general.
  • The majority of Chapter 14 includes assessment items involving operations with polynomials, which most closely aligns to A.APR.A.1. The inclusion of these topics is not mathematically reasonable as some involve expressions with more than two variables and operations builds upon understandings of the number system which are not fully examined until the end of Grade 8.

*Evidence updated 10/27/15

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for spending the majority of class time on the major work of Grade 8. The major work of Grade 8 is to work with radicals and integer exponents (8.EE.A); understand the connections between proportional relationships, lines and linear equations (8.EE.B); analyze and solve linear equations and pairs of simultaneous linear equations (8.EE.C); define, evaluate and compare functions (8.F.A); use functions to model relationships between quantities (8.F.B); understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A); and understand and apply the Pythagorean Theorem (8.G.B). Course 3 of the Holt McDougal series has approximately 20% of its content focused on the major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for spending the majority of time on the major work of Grade 8.

  • The major work of Grade 8 is to work with radicals and integer exponents (8.EE.A); understand the connections between proportional relationships, lines and linear equations (8.EE.B); analyze and solve linear equations and pairs of simultaneous linear equations (8.EE.C); define, evaluate and compare functions (8.F.A); use functions to model relationships between quantities (8.F.B); understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A); and understand and apply the Pythagorean Theorem (8.G.B).
  • Course 3 of the Holt McDougal series has approximately 20% of its content focused on the major work.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
0/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for coherence. There was one lesson where the supporting work enhanced the understanding of the major work of Grade 8. It would take more than 190 days to complete Course 3 and the majority of the lessons are well below Grade 8 standards or address Grade 9 standards. The mathematics progression for Course 3 is based on the National Council of Teachers of Mathematics Curriculum Focal Points instead of the CCSSM.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for the supporting content enhancing the major work.

  • The only lesson that uses a supporting cluster to enhance major work is chapter 4, lesson 7. Students have to know that there are numbers that are not rational, and approximate them by rational numbers (8.NS.A) to support working with radicals and integer exponents (8.EE.A).
  • The rest of the supporting clusters for Grade 8 are taught in isolation from the major work.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for being able to complete Course 3 in a school year.

  • Using the 45-minute lesson planning guide, the course would take more than 190 days to complete. There is minimal time spent on Grade 8 CCSSM.
  • The majority of the lessons are on material well below Grade 8 or are Grade 9 CCSSM.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
0/2
+
-
Indicator Rating Details

The instructional materials for Grade 8 do not meet expectations for being consistent with the progression in the standards.

  • The mathematics progression for course 3 is based on the National Council of Teachers of Mathematics Curriculum Focal Points instead of the CCSSM, thus the grade-by-grade progression of the CCSSM is not reflected in these materials.
  • The materials have a reaching all learners section at the beginning of each chapter but it does not give specific support for teachers on how to differentiate in each lesson. There are pretests for each chapter but in order to use the data to make instructional decisions a teacher would need to have the supplemental materials.
  • The materials don't explicitly relate grade level material to prior knowledge from earlier grades. The same exact lesson is in each of the Grade 6 through Grade 8 texts. This implies that it may be an attempt to link to prior knowledge but without a teacher looking at the other grades this would not be known.
  • There is a math background section for each chapter for the teacher. It gives some general ideas of connections.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
0/2
+
-
Indicator Rating Details

The instructional materials for Grade 8 do not meet expectations for fostering coherence.

  • The mathematics progression is based on the National Council of Teachers of Mathematics Curriculum Focal Points instead of the CCSSM, thus the learning objectives are not visibly shaped by the CCSSM cluster headings.
  • The mathematics taught in this series is done in isolation without connections between clusters.
  • There is also a lot of repetitive work across the grade levels.

Gateway Two

Rigor & Mathematical Practices

Not Rated

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
0/8

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
0/2

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
0/2

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
0/2

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
0/2

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
0/10

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
0/2

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

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.
0/2

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials suggest 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).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

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 Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

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.).
0/0

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.
0/0

Additional Publication Details

Report Published Date: Wed Feb 11 00:00:00 UTC 2015

Report Edition: 2010

Title ISBN Edition Publisher Year
null 9780030994302 null null null
null 9780030994333 null null null

About Publishers Responses

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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.

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Math K-8 Rubric and Evidence Guides

The K-8 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 K-8 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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