Alignment to College and Career Ready Standards: Overall Summary

While Course 1 does address major coursework of Grade 6, future grade level work is taught and assessed. Chapter 7 addresses major work with ratios. However, the material often uses the term “proportion” and asks students to solve for them. This is not wording taken from the standard as students in Grade 6 do not directly solve proportions. Another example of this is seen in Chapter 13 where the material uses the term “function.” This terminology isn’t used until Grade 8. By changing these two terms, the problems on these chapter assessments would more closely align to the Grade 6 standards. Since these materials do not meet the expectations for alignment to the CCSSM for focus or coherence, they were not reviewed for rigor or the math practices.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
1
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 6 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 6, approximately 12 percent of time is dedicated to major work for Grade 6. 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). Less than 50 percent of the resource assesses Grade 6 standards. This number was found by finding the average percent of questions on grade level within each unit assessment.

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 6 do not meet the expectations for assessing materials at the Grade 6 level. Overall, there were too many assessment items that most closely aligned to standards above Grade 6. Examples of these occurrences can be found in chapters 3, 7, 8, 9, 10, 11, 12 and 13.

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 reviewed for Grade 6 do not meet the expectations for appropriately assessing grade-level standards. Overall, the materials assess topics from future grades in such a way that the modification or omission of the assessment items aligned to the above grade-level topics, and the accompanying lessons, would significantly impact the underlying structure of the materials for the grade. A list of the above, grade-level topics and the chapters in which they occur follow.

  • In Chapter 3, there are assessment items that address scientific notation (8.EE.A.4).
  • In Chapter 7, there are assessment items that address working with scale drawings (7.G.A.1).
  • In Chapter 8, there are assessment items that address angle relationships, which most closely align to 7.G.B.5, and transformations, which most closely align to 8.G.A.
  • In Chapter 9, there are assessment items that address parts of circles and the circumference of circles, which most closely aligns to 7.G.B.4.
  • In Chapter 10, there are assessment items that address the area of circles (7.G.B.4), the volume of triangular prisms (7.G.B.6), and the volume of cylinders (8.G.C.9).
  • In Chapter 11, there are assessment items that address transformations on the coordinate plane, which align to 8.G.A, operations with negative, rational numbers, which align to 7.NS.A, and solving equations involving negative, rational numbers, which align to 7.EE.B.
  • In Chapter 12, the vast majority of the assessment items address probability, which aligns to 7.SP.C.
  • In Chapter 13, there are assessment items that address writing functions in two variables, which aligns to 8.F.B.4, and solving multi-step equations and inequalities, which aligns to 7.EE.B.

*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 6 do not meet the expectations for the majority of class time being spent on the major work for Grade 6. Course 1 of the Holt McDougall series has approximately 25% of its content focused on the major work. The major work of Grade 6 is understanding ratio concepts (6.RP.A); applying and extending previous understandings of multiplication and division to divide fractions by fractions (6.NS.A); applying and extending previous understanding of numbers to the system of rational numbers (6.NS.C); applying and extending previous understanding of arithmetic to algebraic expressions (6.EE.A); and representing and analyzing quantitative relationships between dependent and independent variables (6.EE.C).

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 6 do not meet the majority of class time spent on the major work of Grade 6. The major work of Grade 6 is:

  • understanding ratio concepts (6.RP.A);
  • applying and extending previous understandings of multiplication and division to divide fractions by fractions (6.NS.A);
  • applying and extending previous understanding of numbers to the system of rational numbers (6.NS.C);
  • applying and extending previous understanding of arithmetic to algebraic expressions (6.EE.A); and,
  • representing and analyzing quantitative relationships between dependent and independent variables (6.EE.C).

Course 1 of the Holt McDougal series has approximately 25% of its content focused on the major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
1/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectations for coherence. There were a few places where the supporting work enhances the understanding of the major work of Grade 6. It would take more than 190 days to complete Course 1 and the course addresses less than a third of the Grade 6 standards. The mathematics progression for course 1 is based on the National Council of Teachers of Mathematics Curriculum Focal Points instead of the CCSS.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for supporting content enhancing the major work for Grade 6.

  • There were a few places where the supporting work enhances the understanding of the major work of Grade 6. It was less than 10% of the work in Course 1 of the Holt McDougal Series.
  • There is evidence that in a few lessons in chapters 3-6 and 10 that students compute fluently with multi-digit numbers and find common factors and multiples (6.NS.B) to support the major work of 6.EE.A.
  • The work of solving real-world and mathematical problems involving area, surface area and volume (6.G.A) is used to support the major work of reasoning about and solving one-variable equations. Lessons supporting standard 6.EE.B are in chapter 10.

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 6 do not meet the expectations for being able to complete Course 1 in a school year.

  • Using the 45-minute lesson planning guide, it would take more than 190 days to complete this course.
  • These concepts in the lessons would cover less than a third of the Grade 6 CCSS.

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 6 do not meet expectations for being consistent with the progression in the standards.

  • The mathematics progression for Course 1 is based on the National Council of Teachers of Mathematics Curriculum Focal Points instead of the Common Core State Standards, 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 do not 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, but there is no indicator in the materials that this lesson will repeat in future grades.
  • There is a mathematics background section for each chapter for the teacher. It gives a general overview of connections between grade levels.

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 6 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 CCSS, 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 repetitive work across the grade levels. For example, chapter 7 course 1 and chapter 4 course 2 cover almost identical material on ratios, rates and proportions. Chapter 8 in both course 1 and 2 include practically the same geometry information on lines and angles and transformations.

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details

Did not review

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

+
-
Gateway Three Details

Did not review

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 9780030994289 null null null
null 9780030994319 null null null

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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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