## Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 5 do not meet expectations for alignment. The materials do not devote the large majority of time to grade-level work and topics from future grades are assessed. There is little explicit connection made to the progressions of learning in the standards. Since the materials do not meet the expectations for focus and coherence in gateway 1, they were not reviewed for gateway 2.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
2
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

|

## Gateway 3:

### Usability

0
22
31
38
0
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

The instructional materials reviewed for Grade 5 do not meet expectations for focus on major work and coherence at the grade. There are end-of-unit assessments in units 6, 8 and 9 that assess content above the scope of the grade. There is also not enough time spent on the major work of fractions at the grade level, which support important progressions as students move into Grade 6 and begin grappling with understanding ratio reasoning.

### 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 5 do not meet the expectations for assessing material at the grade level. The materials assess many topics that are above grade level, and statistical distributions, specifically, should not be assessed before Grade 6. Other examples include:

• The end of unit assessment in unit 6 asks students to add numbers to tenths, hundredths and thousandths place. This computation is in the standards in Grade 6. There is also too much of an extension of the standard 5.NBT.A.3.B in this assessment. The standard calls explicitly for two decimals to be compared and there are ten decimals to be compared.
• Problem 3 in the unit 8 end of unit assessment is aligned to 6.EE.A.2 since students are asked to more formally evaluate and write expressions.

### 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 5 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.”. There are also many other sessions in the materials that would need to be modified or omitted because of their alignment to above, grade-level standards. For this indicator, all of the identified assessments and end-of-unit assessments for the nine units were reviewed. Units and sessions accompanying above grade-level assessment items are noted in the following list.

• In unit 9, the end-of-unit assessment expects students to: compare sets of data using the shape and spread of the data; draw conclusions based on data; and use operations on fractions to solve problems involving information given in line plots. The scoring rubric indicates that in order to meet expectations, students are to recognize statistical distributions including range, median, mode, and outliers. These expectations align to standards within 6.SP. 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.
• The end-of-unit assessment for unit 4 expects students to use fraction-percent equivalents to solve problems about the percentage of a quantity and order fractions with like and unlike denominators. Expectations on fraction-percent equivalents align to 6.RP.A.3.C. , “Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.” There are nine sessions that align to the expectation on percentages, and these nine sessions could be omitted without affecting the structure of the materials.
• The end-of-unit assessment for unit 6 expects student to: order decimals and justify their order through reasoning about decimal representations, equivalents, and relationships and add decimals to the thousandths through reasoning about place value, equivalents, and representations. The scoring rubric on page 136 indicates that students must be able to add decimals (to the thousandths) in order to be proficient. There is no grid provided, and student exemplars presented all involve actually adding the decimals rather than completing grids. These expectations go beyond 5.NBT.A.3.Bb, “Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons,” and 5.NBT.B.7, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.”. There are 13 sessions that are aligned to the beyond grade-level expectations, and the lessons should not be omitted because that would affect the underlying structure of the materials for the unit.
• The end-of-unit assessment for unit 8 expects students to: use tables and graphs to represent the relationship between two variables; use tables and graphs to compare two situations with a constant rate of change; and use symbolic notation to represent the value of one variable in terms of another variable in situations with constant rates of change. The scoring rubric on page 126 indicates that students must be able to write an expression to represent the value of one variable in terms of another variable. These expectations extend beyond 5.OA.B.3 to more closely align with 6.EE.C.9. , “Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.” There are seven sessions that align to these expectations, and omission, or modification of, these seven sessions would not significantly impact the underlying structure of the materials.

*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 5 do not meet expectations for focus. The materials do not spend the majority of time on the major clusters in the grade. There were lessons in the CCSSM resource that addressed one standard, but that is not adequate time to teach content in major focus areas. There was evidence found where actual student activities do not align with the standards labeled in the materials/table of contents and where students are engaging in work above the grade level, thus diminishing the focus.

### 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 5 do not meet expectations for focus. There are 161 sessions between assessments and lessons in the materials. While 117 of the lessons are labeled as aligned to the major work with a percentage of 72% based on the labeled alignments from the publisher, there are many instances where the actual work in the lessons is not accurately aligned to the standard as marked. Examples include:

• In unit 2, lesson 1.1 has work with nets, a Grade 6 standard.
• In unit 2, lesson 2.3 has students measuring cubic units in their classroom. There is no way to guarantee that these will be whole number values when working with volume and therefore is above the scope of Grade 5.
• In unit 7, lesson 1.1 and 1.3 are both labeled as 5.NF.A.2 but do not address word problems involving +/- of the same whole.
• Unit 4, session 1.1 is labeled as aligned to 5.NF.A.1, but goes beyond the scope of that standard into percent work and portions of a set and a whole. This is not aligned to 5.NF.A.1 but rather to 6.RP.
• In unit 4, 12 lessons are labeled solely to a math practice, and diminish focus on the major work of the grade.
• Unit 5 has seven lessons that are labeled solely to a math practice and not a content standard in the grade. This lack of alignment interferes with a focus on the major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
2/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 do not meet expectations for coherence in the grade. The materials are not coherent with the progressions, as decimal work goes beyond the scope of the grade and there is inconsistent alignment and coherence within the standards.

### Indicator 1c

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

Instructional materials reviewed for Grade 5 do not meet expectations for coherence because the content in the materials does not support focus and coherence. Overall, the review team concluded that there were very few lessons that had supporting/additional clusters to support the major work. For example:

• In unit 9, lessons 1.1-1.4 are labeled as 5.MD.B.2, but the data measurements are whole numbers so there a misalignment with the standard. These do not support the work of 5.NF.A.
• Unit 8, lessons 1.1-1.3 and 2.5-2.6 examined for 5.OA.B.3 with connections to 5.NBT fluency unearthed misalignments with constant rate and doubling patterns that are beyond the grasp of Grade 5, diminishing the coherence between additional/supporting and major work at the grade. These lessons were also labeled as connected to 5.G.A which does not appropriately align to the coordinate system work of the grade.
• Content aligned to a math practice, rather than a content standard, in units 4 and 6, do not support connections within the grade level content.

### 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 instructional materials reviewed for Grade 5 partially meet expectations for viability of content for the scope of one year. The curriculum consists of 161 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, with the inclusion of unit 4 on proportions, the review team determined that the amount of content was not fully viable for one school year to foster coherence between grades. Of particular concern is that 11 sessions out of 161 are aligned to standards in the 5.MD.C cluster, all in unit 2. Since this is one of five major clusters in the grade there is not enough time spent to develop understanding of the content within the 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

The instructional materials reviewed for Grade 5 do not meet expectations for consistency with the progressions. The materials do not develop according to the progressions, nor do they give students extensive work with grade-level problems. In addition, while there are teacher notes in the "Looking Back" section of each unit, there is not explicit connection to specific standards addressed in prior grades. For example:

• This grade includes 19 lessons that are only aligned to the mathematical practices. This is a red flag that the lessons do not develop with a grade-by-grade progression because the material is not labeled as aligned to any grade-level work. These lessons are in Investigations 1-3 in unit 4 and Investigation 2 in unit 5.
• Unit 4 includes 11 lessons that are misaligned and teach percent, a Grade 6 standard.
• Within any standard, there are no examples of a two-step story problem.
• The domain 5NF, which is a major work, is greatly under-represented in this series. It is taught piecemeal across units 4-6, and in two new CCSM-aligned lessons in unit 9. These are aligned to 5NF.6 as are four new CCSSM lessons in unit 4. Six lessons on multiplication of fractions and mixed numbers does not support the consistent progression of the standards.
• There are no instances when CCSSM from earlier grades are labeled in the materials.

### 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 5 partially meet expectations for fostering coherence through connections at a single grade. The materials include some instances where learning objectives are shaped by cluster headings and include some problems that connect clusters and domains. For example:

• With 19 lessons in units 4 and 5 aligned to math practices and not grade level content, these lessons do not support alignment with cluster headings and connections between clusters.
• Lessons 3.A8 and 3.A9 in unit 6 represent lessons aligned to content where the conversions with the metric system can be an important practical application of the place value system. Students' work with these units (5.MD.A.1) were not fully connected to their work with place value (5.NBT.A.1). The math focus points only reference converting measurements within a given measurement system.

There were examples, however, where grade level content was appropriately aligned to support a partial rating in the indicator.

• For example, fraction multiplication in 5.NF.B includes interpretation of the meaning of multiplication when multiplying two fractions. This has the potential to connect to 5.NBT.B.5, whole number fluency. Since fluency stems from conceptual understanding, when students are asked to interpret products in lesson 4A.4 in unit 4, they are showing conceptual understanding that will build to fluency.

## Rigor & Mathematical Practices

### 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

## Usability

### 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

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

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

Report Edition: 2012

Title ISBN Edition Publisher Year
null 9780328687176 null null null
null 9780328697564 null null null

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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