|

## 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
N/A
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## Gateway 3:

### Usability

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

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Does Not Meet Expectations

+
-
Gateway One Details

### Criterion 1a

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

Grade 4 Math in Focus materials assess topics from future grade-level content. Chapters 2, 4, 5, 6, 7, 8, 14 and 15 all contain future grade level assessments. Chapters 5, 14, and 15 assess statistical distributions and similarity, congruence, and transformations.

Review Team Note: The assessments are included in the teacher edition, but are printed at a small scale: ⅛ of a page. Since the assessments are not included in the student edition and are so small in the teacher edition, an additional assessment book would need to be purchased or teachers would need to reproduce the assessments.

### 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 the Grade 4 Math in Focus do not meet the expectation for this indicator due to assessment of statistical distributions and similarity, congruence, and transformations. Additionally, there are several instances where future grade level work is covered and assessed. The following evidence describes both the chapter tests and the chapter reviews.

• In chapter 5, all questions from the assessment assess Grade 6 material of mode, mean and median (items 1-12).
• In chapter 14, questions 5, 7, 8, 11 and 12 assess rotational symmetry.
• In chapter 2, questions 4, 8 and 10 assess greatest common factor and least common multiple, which is a Grade 6 standard.
• The chapter 4 assessment contains questions (items 3, 4, 9, 10, 11 and 12) on line graphs.
• The chapter 7 assessment contains question on decimals including reading, writing, comparing and converting fractions to decimals (items 1-10).
• In chapter 8, the assessment contains questions on addition and subtraction of decimals, which is a Grade 5 standard (items 1-12).
• Benchmark 2 test contains questions on decimals (items 1, 2, 3, 4, 5, 11, 12, 13, 14 and 21)

*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

Students and teachers using the Grade 4 Math in Focus materials would not devote a large majority of the time to the major work of the grade. Approximately 33% percent of the time was spent on the major work of the grade. More time is spent on off grade-level work than on the major work of the grade. Overall, the materials did not provide the majority of time on the major work of the grade level.

### 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. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 and on future grade level work.

• Five out 15 chapters (1, 3, 6, 7 and 8) or about 33% of the time is focused on the major work of the grade.
• Six out of 15 chapters (2, 9, 10, 11, 13 and 14) or about 40% of the time is focused on the supporting work of the grade.
• Three chapters (4, 5 and 15) or about 20% of the time is focused on work not related to grade level.
• The content of chapter 4 does not meet the full intent of Grade 4 work. The Grade 4 standard for line plots uses fractions of a unit, and in chapter 4, line plots with whole numbers are the only ones present.
• The content of chapter 5 focuses on probability, which is a Grade 6 standard.
• The content of chapter 15 focuses on tessellations, which are not addressed directly in the standards; however, to complete tessellations students must understand rotations, reflections, and translations, which are Grade 8 standards.
• There are 118 days of instruction. 24% (28 days) are spent on major work, 19% (22 days) are spent on supporting work, 23% (27 days) are spent on additional work, and 34% (41 days) are spent on work that is in another grade level.
• There are 59 instructional lessons in Grade 4. Thirteen lessons, or 22%, are spent on major work, 24% (14 lessons) are spent on supporting work, 15% (9 lessons), and 39% (23 lessons) are spent off grade level.
• More time is spent on off grade-level work than is spent on the major work of the grade.
• The large amount of future grade level work that is introduced and assessed in the material detracts from the major work of the grade.

### 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 expectation of coherence and consistency The materials do not represent a full year of content. Additionally, 41 of the 119 days are spent on future grade level work. Teachers using the materials would not be providing their students with extensive work in grade level problems, since only about 65% of the lessons focus on grade-level problems. Due to the amount of future grade level content, the materials are not able to develop according to the progressions of the Standards. Overall coherence and consistency of the standards is not achieved in Grade 4 Math in Focus.

### 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 supporting content does not enhance the focus and coherence by engaging students in the major work of the grade. For this indicator, all grade level work that was not major work was considered supporting work. Chapters 2, 9, 10, 11, 13 and 14 represent supporting work of the grade.

• Chapter 2 includes lessons 2.2, 2.3 and 2.4 where the major work of the grade is supported using the four operations.
• The content in chapters 9, 10, 11 and 14 is treated separately from the major work of the grade level.
• In chapter 13 only lesson 13.1 supports the major work of the grade by using fractions.

### 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 amount of content designated for Grade 4 Math in Focus is not 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.

• There are 59 lessons in the program that cover only 119 days of instruction, many of which are not spent on the major work of the grade.
• This falls about 56 days short of the typical school year.

### 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

Grade 4 Math in Focus materials are not consistent with the progressions in the standards. Content is not clearly identified, there are not extensive grade-level problems and concepts are not explicitly related to prior knowledge.

Materials do not develop according to the grade-by-grade progressions and prior and future grade content is not clearly identified.

• Several chapters are above grade level work and are not identified as such in the program, including the teacher and student editions.
• The content in chapter 5 is Grade 5 work, and in the skills trace (found at the front of each chapter) and in the chapter planning guide (found in each chapter) there are not notations explaining how the work is Grade 5 work or how this is related to grade-level work. The same is true of chapters 4, 6, 8 and 15.

Materials do not give students extensive work with grade-level problems.

• Grade 4 Math in Focus has 55 lessons that span approximately 119 days.
• Thirty-six lessons or about 65% of the time is spent on grade-level problems.
• Nineteen lessons or about 35% is spent on work other than grade-level problems.
• On a positive note, students have at least four guided practice problems followed by at least 10 independent practice problems in each lesson.
• Thirty days include work that is not grade level appropriate.
• Four days are spent on work that is not in the CCSSM.

Materials do not explicitly relate grade level concepts to prior knowledge from earlier grades.

• Each chapter contains an initial lesson called "Recall Prior Knowledge." In this lesson, students are recalling prior knowledge from earlier grades and chapters.
• Students are recalling prior knowledge from earlier grades and chapters but it does not directly always trace back to the standards. For example, chapter 6 states "students learned in Grade 3 to express fractions in simplest form, and to add and subtract like fractions;" however, there is not a Grade 3 standard which addresses this skill. Students in Grade 3 are not asked to add and subtract like fractions. The closest Grade 3 standard 3.NF.A.3.B states "Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model."
• If prior knowledge were aligned to the standards and not the text then CCSSM concepts would be explicit. Instead skills and strategies from the series are explicitly referred to in the prior knowledge section.
• Chapter 12 refers back to another chapter in Grade 4 instead of tracing the standard from prior 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

Materials do not foster coherence through connections at a single grade level. The learning objectives are not clearly linked to the CCSSM cluster headings, and the materials do not connect two or more clusters in a domain.

The Grade 4 materials do not include learning objectives that are visibly shaped by CCSSM cluster headings.

• For example in chapter 5, the objectives are to describe a data set using the average or mean and then find the mean, median, mode and range of a set of data. This is not a Grade 4 standard within the CCSSM.
• There is a section in the teacher guide for Grade 4 that indicates CCSSM correlations, however these are not always a correct alignment.
• However, the scope and sequence is not organized by cluster headings in Grade 4.
• There are many chapters that are do not address the learning objectives of CCSSM cluster headings (chapters 4, 5, 6, 8 and 15).

The Grade 4 materials do not include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

• The chapter planning guide contains several references in each lesson from two or more clusters and/or two or more domains; however, a closer look at the activities shows the activities do not truly align to the stated standards.
• For example, chapter 1 lesson 1 states it aligns to both 4.NBT and 4.OA. However, when looking at the lesson it does not ask students to generate a number or shape pattern that follows a given rule.
• A missed opportunity to make connection with finding the area of a rectangle (4.MD.2) and multiplying a fraction by a whole number (4.NF.4).
• The content in chapter 9 misses the opportunity to connect measurement of angles (4.MD.C) with addition of fractions (4.NF.3).

## Rigor & Mathematical Practices

#### Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

### Criterion 2a - 2d

Rigor and Balance: 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.

### 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.
N/A

### 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.
N/A

### 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
N/A

### 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.
N/A

### Criterion 2e - 2g.iii

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

### Indicator 2e

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

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
N/A

### Indicator 2g

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

### 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.
N/A

### 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.
N/A

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
N/A

## Usability

#### Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

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

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

There is variety in 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.
N/A

### Indicator 3d

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

### Indicator 3e

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

### Criterion 3f - 3l

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

### Indicator 3f

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

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

Materials contain a teacher's edition (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.
N/A

### 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.
N/A

### 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).
N/A

### 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.
N/A

### Indicator 3l

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

### Criterion 3m - 3q

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

### Indicator 3m

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

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

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

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### 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.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

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

### Indicator 3r

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

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

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

### Indicator 3u

Materials 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).
N/A

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

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

### Indicator 3y

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

### Criterion 3aa - 3z

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

### 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.
N/A

### Indicator 3ab

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

### Indicator 3ac

Materials can be easily customized for individual learners. 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.
N/A

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2015/02/15

Report Edition: 2013

Title ISBN Edition Publisher Year
9780544224261
9780544224278

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria 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 review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria 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.

## Math K-8

K‑8 Evidence Guide K‑8 Review Criteria

Kindergarten assessments were not reviewed because they are not included in the materials.  The assessment book is available for purchase separately from the main materials.  Grades 1 and 2 assessments were reviewed.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.