Alignment to College and Career Ready Standards: Overall Summary

The materials reviewed for Grade 6 do not meet the expectations for alignment to the CCSSM. In terms of focus and coherence, there were many concepts assessed that are beyond the Grade 6 CCSSM, and the instructional materials reviewed for Grade 6 had approximately 52 percent of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 6.EE.C. The content could be covered in 155 days. There are areas where the materials have strong connections and areas that could be stronger. In the teacher’s and the student’s edition, the CCSSM are listed for each lesson and are tied to the CCSSM. Since the materials do not meet expectations for alignment in focus and 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
6
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 materials reviewed for Grade 6 do not meet the expectations for focusing on major work and coherence. There were many concepts assessed that are beyond the Grade 6 CCSSM, and the instructional materials reviewed for Grade 6 had approximately 52 percent of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 6.EE.C. However, this content could be covered in 155 school days. There are areas where the materials have strong connections and areas that could be stronger. In the teacher’s and the student’s edition, the CCSSM are listed for each lesson and are tied to the CCSSM.

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 expectations for assessing material at the Grade 6 level. There are too many concepts assessed that are beyond the Grade 6 CCSSM, and the alteration or omission of these items would significantly impact the structure of the materials. In chapters 8, 9 and 11, there are assessment items that most closely align to standards above Grade 6, and their inclusion is not mathematically reasonable for Grade 6. The alteration or omission of these items would significantly impact the underlying structure of the materials.

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 6 do not meet the expectations for assessing materials at the Grade 6 level. There are some assessment items that align most closely to standards above Grade 6 whose inclusion is mathematically reasonable. However, there are too many items that align most closely to standards above Grade 6 whose inclusion is not mathematically reasonable and whose alteration or omission would significantly impact the underlying structure of the materials.

  • In Chapter 1, square roots and cube roots, which most closely align to 8.EE.A.2, are assessed with a few items. The inclusion of these items is mathematically reasonable as they are introduced along with numerical expressions that contain whole-number exponents.
  • In Chapter 5, there are assessment items that examine students’ knowledge of extended ratios. The inclusion of these items is mathematically reasonable as they are introduced along with ratios that contain only two quantities.
  • The Chapter 6 test has a few problems on sales tax, simple interest, markup, and discounts, which align to 7.RP.A.3. The inclusion of these items is mathematically reasonable as they are introduced along with items that align to Grade 6 standards.
  • In Chapter 8, there are assessment items with inequalities that include “equal to.” Although this is only a slight extension of the Grade 6 standards, this inclusion introduces confusion for students as they are initially learning and understanding the similarities and differences between algebraic equations and inequalities. This confusion makes the inclusion of inequalities that are not strict mathematically unreasonable.
  • In Chapter 9, there are assessment items asking students to classify quadrilaterals that do not have vertical or horizontal sides. To classify quadrilaterals without horizontal or vertical sides would require students to calculate distances using a method that is beyond Grade 6 standards. The inclusion of this extension is not mathematically reasonable as it could detract from the understandings Grade 6 students are developing concerning distance between points in the coordinate plane.
  • The vast majority of Chapter 11 has questions that assess finding the area and circumference of circles, which aligns to 7.G.B.4. The inclusion of these items is not mathematically reasonable, and the omission or alteration of the chapter would significantly impact the underlying structure of the materials.
  • Chapter 12 has a very small number of questions that assess the volume of a triangular prism, which aligns to 7.G.B.6. The inclusion of these items is mathematically appropriate as they are introduced with items that align to Grade 6 standards.

*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 spending the majority of class time on the major clusters for Grade 6. The instructional materials reviewed for Grade 6 have approximately 52% of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 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 expectations for spending the majority of class time on the major clusters for Grade 6.

  • The instructional materials reviewed for Grade 6 had approximately 52% of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 6.EE.C.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The materials reviewed for Grade 6 partially meet the expectations for coherence. The content could be covered in 155 days. There are areas where the materials have strong connections and areas that could be stronger. "Concepts" and "Skills Across the Curriculum" link the current material to the skills progression to both the previous and the next grade. In the teacher edition the CCSSM are listed for each lesson. In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.

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 the supporting content enhancing the major work.

  • There are areas where the materials have strong connections and areas that could be stronger.
  • Lesson 3.3 connects the work of greatest common factor to dividing fractions.
  • Lesson 3.4 connects operations with decimals to dividing fractions.
  • Lesson 9.3 connects solving real-world problems on coordinate graphs with using formulas and rates.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 partially meet the expectations for the amount of content designated being viable for one school year.

  • The content could be covered in 155 days.
  • While overall it is viable for a school year, the amount of time on the major work for Grade 6 is less than 65% of the year, and teachers would need to find supplemental materials in order to cover the content required for Grade 6.

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.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 meet the expectations for the progressions in the standards.

  • "Concepts" and "Skills across the Curriculum" link the current material to the skills progression to both the previous and the next grade.
  • Every lesson has the CCSSM identified, even if the standards are from different grade levels.
  • The Grade 6 lessons 1.4 and 1.5 on square and cube roots are connected to Grade 8 8.EE.A.
  • In Grade 6, chapter 11 is on circles, which is identified as a Grade 7 standard.
  • Every chapter starts with a section of recalling prior knowledge for the students with a review and a quick check practice.
  • Math background pages give teachers a review of the background knowledge needed for the unit.

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.
2/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 meet the expectations for fostering coherence through connections at a single grade.

The CCSSM are listed for each lesson within the teacher edition.

The lesson objectives in the student edition are based on the CCSSM and are listed next to each lesson.

Connections are evident between two or more clusters in a domain or two or more domains:

  • Lessons 7.1 and 7.3-algebra expressions-each connect two cluster headings, 6.EE.A and 6.EE.B.
  • Lesson 3.4-word problems with fractions and decimals-connects two cluster headings, 6.NS.A and 6.EE.B, though one of them is additional work.
  • Lessons 8.1 and 8.2-algebra equations-connect the cluster headings 6.EE.A, 6.EE. B and 6.EE.C.
  • All of Chapter 9 on the coordinate plane connects domains such as 6.NS.C, 6.G.A, 6.EE.A and 6.RP.A.
  • Lesson 10.1-area of triangles-connects domains 6.EE.A and 6.G.A.
  • Chapter 12-surface area and volume-connects domains 6.EE.A and 6.G.A.
  • Lesson 13.1-collecting data-connects cluster headings 6.SP.A and 6.SP.B.
  • Chapter 14-mean, median, mode-connects cluster headings 6.SP.A and 6.SP.B.

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: Sun Feb 15 00:00:00 UTC 2015

Report Edition: 2013

Title ISBN Edition Publisher Year
null 9780547618098 null null null
null 9780547618128 null null null

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.

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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