Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 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.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

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

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 expectations for focus on major work and coherence. The materials do not devote the large majority of time to grade-level work, especially with the inclusion of Unit 7 which is aligned to above grade-level work. In addition, there is no explicit connection made to standards from prior or future grades, fostering 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 material at the grade level. The materials assess many topics that are above grade level. Statistical distributions, specifically, should not be assessed before Grade 6.

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.”. 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 2, the end-of-unit assessment expects students to describe the shape of the data from a numerical data set, including where the data are concentrated and the highest, lowest, and median values. 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.
  • Problem 2 in the end-of-unit assessment for unit 4 assesses how to find the area of polygons, in this case a kite-shaped figure, using square units. The scoring rubric on page 161, indicates that the question is assessing student ability to find the area of polygons using a square unit of measure and counting them– square units and half units. Finding the area of shapes other than rectangles aligns to 6.G.A.1. , “Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.” This problem could be omitted from the assessment without impacting the structure of the assessment.
  • The end-of-unit assessment for unit 7 expects students to clearly show an understanding of volume from the scoring rubric on page 106. This expectation aligns to 5.MD.C, “Geometric measurement: understand concepts of volume,” and all of the sessions in unit 7 could be omitted without significantly impacting the underlying structure of the materials.
  • Problem 2 on the end-of-unit assessment for unit 8 expects students to solve division problems with 1-digit and 2-digit divisors by using at least one strategy efficiently. The scoring rubric on page 128 indicates that there are several strategies students could use to demonstrate proficiency (none of which is the standard division algorithm). The inclusion of 2-digit divisors goes beyond the language of 4.NBT.B.6, and the problem could either be omitted or modified to a 1-digit divisor without impacting the structure of the assessment.
  • In Unit 9, all problems on the end-of-unit assessment are on the topics of line graphs, constant change, and representing constant change on tables. The scoring rubrics on page 145 indicate that students must be able to read and interpret line graphs involving constant rate of change and to complete tables based on a constant change and represent it with an arithmetic expression. Constant rate of change is a topic that aligns to 6.RP.A., “Understand ratio concepts and use ratio reasoning to solve problems.” Since this is the last unit of the grade-level materials, this unit could be omitted without affecting the 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 4 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 book 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

Instructional materials reviewed for Grade 4 do not meet expectations for focus. The majority of class time is not spent on the major clusters of the grade. According to the alignment 62% of the time is spent on major work at the grade. Upon deeper examination of the content in the nine units at the grade level, in five of these units (2, 4, 5, 7 and 9) there is above grade-level content that is being taught and assessed, which accounts for a portion of each of these not being fully aligned. This would even further decrease the amount of material on major work of the grade. For example:

  • Lesson 1.1 and 1.2 in unit 9 align with 8.F.
  • Lesson 2.4 in unit 9 graphs a linear pattern-Grade 5 work-and in lesson 2.7 the work comparing the two quantities that are graphed with possible expressions and equations is Grade 6 work.
  • Unit 7 has 13 lessons and three assessments. Of the 13 lessons, only two are truly aligned to the standards. Lesson 3.1 in investigation 3 is only aligned because five problems on the homework page ask for students to compare fractions to hundredths, the remaining three problems on the page that ask for decimal addition are not aligned and the lesson itself is on volume and nets, which is Grades 5 and 6 work.

Additionally, every 4.NF standard, which is major work at the grade, is covered in unit 6, with two additional lessons (3.1 and 3.2) in unit 7. The two lessons from unit 7 do not match to 4.NF.C.7 and were not included in the following calculation. Therefore in the fraction unit, there are 22 lessons out of 162 total lessons in the program, which allots for 13.5 % of the time, or 15% including the three assessments of fraction. With six major clusters in Grade 4, three of them being 4.NF.A, B and C, this is not enough time to spend on the work of extending equivalence, building fractions and understanding decimals.

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 4 do not meet expectations for coherence in the grade. The materials are not coherent with the progressions because work from Grade 5 volume is included and fraction work is underrepresented.

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 4 partially meet expectations for supporting content to enhance focus and coherence simultaneously by engaging students in major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level and in others, it does not. For example:

  • Work in line plots in unit 2 does not support the major work of 4.NF.A and B because they do not involve fractions and the only focus is on the shape of the data.
  • In unit 6, session 2.7A, a line plot with fractional measures is used to solve problems with operations (addition and subtraction) on fractions, thereby connecting 4.MD.B.4 to 4.NF.B.3.
  • In unit 3, work with multiples in investigation 3 and understanding the effect of multiplying by a multiple of 10 supports students in the partial products and other multiplication strategies they will be using when performing multi-digit multiplication and even when using the standard algorithm. This illustrates that work in 4.OA.B supports the major work in 4.NBT.B.4 and 4.NBT.B.5.
  • Unit 4 lessons 1.1-1.5 do not fully support 4.NBT.B.4 as truly developing fluency for adding and subtracting within one million.
  • In unit lessons 4 and 3.1-3.3 students write equations and add and subtract angle measures aligning to 4.MD.C, connecting the work in this standard to computation in 4.NBT.B. These are not, however, in real-world problems.
  • In unit 9, fast and slow growth in lesson 3.1 does not fully support 4.NF standards, nor is the data truly a set of measurements in fractions of a unit where students are solving problems with the fractional measurements displayed.
  • In unit 9 lesson 3.2 also labeled as aligned to 4.MD.B.4 supports work above the grade level (shape of the data, comparisons) and does not foster coherence within Grade 4.
  • Two-step story problems are not evident in the materials. This does not foster coherence nor does it support focus of the grade level.

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 expectations for viability of content for the scope of one year. The curriculum consists of 162 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, the review team found that the major work accounts for about 62% of the lessons. The major work of 4.NF is greatly underrepresented in this series. In addition, unit 6 teaches addition of decimals which is above the grade level in three of the 24 lessons that deal with 4.NF.A, 4.NF.B and 4.NF.C.

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 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 the front matter of each unit, there are detailed explanations of the content addressed that appears in a section called mathematics in this unit. Within this section, the "Looking Back" and "Looking Forward" pieces explains content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. For example:

  • "Understanding Volume" in unit 7, investigation 3, does not follow the grade-to-grade progression due to the concept being misaligned. Volume is introduced as a standard in Grade 5.
  • Investigation 4 in unit 4 is completely not in the grade-to-grade progression because it has lessons on finding the area of special quadrilaterals which is a Grade 6 standard.
  • The major work of 4.NF is greatly underrepresented in this series. There are only 22 of 162 sessions that appropriately support number fraction work.
  • Unit 6 includes language around extending equivalence understanding in number fraction from Grade 3. There is a small note on page 10 about connections to Grades 2 and 3, but not an explicit connection to the standards. These connections could be enhanced in the next edition.
  • In the area of 4.OA.A, only one lesson is focused on multiplicative comparison and this isn't enough to engage the students in this major work. There is an all-around lack of multi-step problem opportunities throughout. For the most part, students are guided through a three-part progression to guide them to solve.

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 4 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:

  • In unit 1, sessions 1.1-1.4 have math focus points mentioning arrays, yet the lessons are aligned to the 4.OA.A domain, whereas a 4.NBT alignment might be more appropriate.
  • Unit 1, sessions 2.2-2.3 have math focus points that use the specific terminology of "fluency," however fluency standards in Grade 4 are specific to addition and subtraction, but the work is on multiplication.
  • In unit 6, the objectives are not clearly shaped by the cluster heading. Most mention adding or subtracting fractions, but do not reference anything that can be tied to extending previous understandings of whole number computation.
  • There is evidence to show that students' work with units of measurement conversion (4.MD.A.1) is connected with the multiplicative comparison work (4.OA.1). In unit 7 session 3.5A, the lesson description includes cues to teachers to discuss how measurement equivalents charts tell how different units are related. For example, "The first equation in the chart (1 pound = 16 ounces) tells you that there are 16 ounces in a pound. That means a pound is 16 times as heavy as an ounce," thereby relating to a multiplicative comparison.
  • No evident connections between multiplicative comparison and the multiplication of a fraction by a whole number (4.NF.B.4) is found in the pertinent lessons (unit 6, sessions 3.A.1-3.A 2).
  • There is also evidence to show that a connection is made between addition of fractions (4.NF.B.3) and angle measurement (4.MD.C.5) in unit 4 session 3.4.A, where an angle measure of 1 degree is related to being 1/360th of a circle when discussing measuring with a protractor.

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: Wed Feb 11 00:00:00 UTC 2015

Report Edition: 2012

Title ISBN Edition Publisher Year
null 9780328687169 null null null
null 9780328697557 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.

X