Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 do not meet the expectations for alignment to the CCSSM.

The materials failed to meet the criteria of gateway 1, where they were reviewed for focus on the major work of the grade and for coherence. The materials assess above Grade 4 standards in a way that negatively impacts the structure of the materials and do not allocate a large percentage of instructional materials to major standards of the grade. Some positive evidence was noted in the coherence criterion, but too many areas of weakness lead to the instructional materials not meeting quality expectations for coherence. Due to the materials not meeting expectations for focusing on major work and coherence, they were not reviewed for rigor and Mathematical 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 4 do not meet the expectations for alignment to focusing on major work of the grade and coherence. The instructional materials do not meet expectations for the two focus criterions because the materials assess standards above Grade 4 in a way that negatively impacts the structure of the materials. The materials do not allocate a large percentage of instructional materials to major standards of the grade. Some positive evidence was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet the quality expectations for coherence.

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 4 do not meet the expectations for assessing grade-level content. Examples of above grade-level standards being assessed can be found in the materials for units 1, 5, 6, 9, and 10. Overall, the omission or modification of lessons that align to the above, grade-level assessment items would create a significant impact on the underlying structure and intent 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 reviewed for Grade 4 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A , “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions”, and they assess similarity, congruence and geometric transformations with questions that align to 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. There are also many other lessons in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. Units and lessons accompanying above grade-level assessment items are noted in the following list.

  • In unit 1, lessons 3, 4, and 5 have assessment items that align to standards from 6.SP.A, “Develop understanding of statistical variability”, and 6.SP.B, “Summarize and describe distributions”. The Key Assessment Opportunities Chart shows the expectation that students be able to find the median of a data set represented in a table, graph, or line plot and make predictions and generalizations about a set of data using the median. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6. These lessons account for seven to eight class sessions of the first unit, which encompasses 12 to 14 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
  • In unit 5, lessons 2, 3, 4, and 5 have assessment items that align to standards from 6.SP.A , “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.” . The Key Assessment Opportunities Chart shows the expectation that students be able to draw a best-fit line; find the median and mean of a data set; and make predictions and generalizations using medians and means. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6. These lessons account for 10 to 12 class sessions of unit 5, which encompasses 16 to 19 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
  • In unit 6, the midterm assessment is lesson 8, which has assessment items that align to standards from 6.SP.A and 6.SP.B, but these items could be omitted without affecting the structure of the assessment or unit.
  • In unit 9, lessons 10 and 11 have assessment items that align to standards from 5.G.B, “Classify two-dimensional figures into categories based on their properties,”, and 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. The Key Assessment Opportunities Chart shows the expectation that students be able to classify two-dimensional shapes using their properties; identify congruent shapes; and identify slides, flips, and turns of shapes. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of similarity, congruence, or geometric transformations should not occur before Grade 8. These lessons account for three to five class sessions of unit 9, which encompasses 16 to 21 class sessions total, so the omission of these lessons would have a minor impact on the structure of this unit.
  • In unit 10, lesson 5 has assessment items that align to standards from 5.G.A “Graph points on the coordinate plane to solve real-world and mathematical problems,” and 6.EE.C, “Represent and analyze quantitative relationships between dependent and independent variables.”. The Key Assessment Opportunities Chart shows the expectation that students be able to name variables in an investigation and make a point graph using ordered pairs with decimal values. This lesson accounts for three to four class sessions of unit 10, which encompasses 13 to 17 class sessions total, so the omission of these lessons would have a minor impact on the structure of this unit.

*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 4 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. A large amount of time is devoted to off grade-level expectations both above and below Grade 4, and very little time is spent solving problems involving the four operations. Only three units out of the 12 (or 25%) are focused on the major work of the grade, units 6, 8 and 10. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 or on standards that are not in Grade 4.

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 4 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. The instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 or on standards that are not in Grade 4.

  • A large amount of time is devoted to off grade-level expectations both above and below Grade 4, and very little time is spent solving problems involving the four operations.
  • The majority of the curriculum is not focused on the major work of the grade. The four operations are absent, and only three units out of the twelve (or 25%) are focused on the major work of the grade, units 6, 8 and 10.
  • Majority of the materials is not on the major work of Grade 4 as a large amount of time includes above grade-level 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 4 do not meet the expectations for being coherent and consistent with the CCSSM. The instructional materials have a very few instances of supporting work fostering coherence, but the amount of content designated for Grade 4 is not viable for one school year. Also, the instructional materials are not consistent with the progressions in the CCSSM, and they do not foster coherence through connections at a single grade. Overall, the instructional materials for Grade 4 exhibit some characteristics of coherence, but for the entire criterion, there are too many weaknesses for the materials to meet the expectations.

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 4 do not meet the expectations for having the supporting content enhancing focus and coherence simultaneously. Overall, the instructional materials miss opportunities to connect non-major clusters of standards to major clusters, and as a result, the supporting content does not engage students in the major work of Grade 4.

  • Supporting content is treated separately and is not used to support the major work of the grade. An example of this is factors and multiples, which is handled separately and does not support the major work of the grade.
  • The expectations do not align or support major clusters for 4.NBT.A or 4.NBT.B. In the answer key, there is not one problem that asks students to do multi-digit arithmetic to solve problems.
  • The expectations of unit 9 do not connect to 4.NF.A-4.NF.C, the major work of the grade.
  • Some of the expectations for unit 1 involve finding the median of a data set and using coordinate pairs, which are above Grade 4 standards.

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 4 do not meet the expectations for having an amount of content designated for one grade level as viable for one school year. Overall, the amount of time needed to complete the lessons is not appropriate for a school year of approximately 170-190 days.

  • The content is designed for 220 days, which exceeds the amount of content that can be taught or learned in a school year.
  • There are 98 lessons in 13 units, designed for 220 instructional days.

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 reviewed for Grade 4 do not meet the expectations for having materials that are consistent with the progressions in the CCSSM. Materials do not give students extensive work with grade-level problems, and grade-level concepts are not always explicitly related to prior knowledge from earlier grades. Also, the materials do not develop according to the grade-by-grade progressions, with non grade-level content not being clearly identified.

  • The off grade content is not clearly identified or related to the grade-level work as evidenced by lessons 3 and 5, unit 1; lesson 3, unit 5; and lesson 8, unit 9.
  • Because of the amount of time spent on off-grade level work, students are not given extensive work with grade-level problems as seen in units 1, 3, 5, 6, 9, 10 and 13.
  • There is no evidence of differentiation for below or above level students. All students and all learning levels are not accounted for.
  • There are no explanations provided for the teacher or student linking prior knowledge from prior grades. For example, unit 12 focuses on division-which is introduced in Grade 3-but the materials do not make an explicit connection to material covered in prior grades.
  • Other examples are units 4 and 11 where connections to prior grade-level concepts exist, but the connections are not explicitly made.

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 reviewed for Grade 4 do not meet the expectations for having materials foster coherence through connections at a single grade. Materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings, and the materials do not always connect two or more clusters in a domain or two or more domains in a grade when appropriate.

  • It is not clear the learning objectives have been shaped by the cluster headings due to the amount of off grade level objectives.
  • The student guides and "at home practice" are not labeled with objectives.
  • The instructional materials do not connect clusters or domains in the grade level. Clusters and domains are treated separately.
  • Units are compartmentalized and lack connections amongst them.

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: Fri Feb 13 00:00:00 UTC 2015

Report Edition: 2015

Title ISBN Edition Publisher Year
null 9781465224149 null null null
null 9781465224255 null null null
null 9781465224309 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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