Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 do not meet the expectations for alignment. The amount of time spent on major work is not consistent with the expectations for focus and the materials include assessment questions above grade-level content. The instructional materials do not attend to Mathematical progressions and, therefore, do not meet the expectations for coherence. All three teacher editions (traditional, STEM, literacy/arts) do not meet the expectations for coherence at Grade 4. The materials do not meet the expectations for focus and coherence in gateway 1 and were not reviewed for gateway 2.

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 indicators 1a and 1b. The amount of time spent on major work is not consistent with the expectations for focus and the materials include assessment questions above grade-level content. The instructional materials do not attend to mathematical progressions and, therefore, do not meet the expectations for coherence. All three teacher editions (traditional, STEM, Literacy/Arts) do not meet the expectations for coherence or focus in Grade 4.

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 topics that are in future grades. The content assessed in Rocket Apogee, STEM Project, is more appropriately aligned with high school, such as HSG.SRT.C.6 and HSG.SRT.C.8 when students are asked to find angle measurements of right triangles using the tangent ratio and Grade 6, such as 6.SP.B.5.C when students are asked to identify outliers and find the averages.

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

Materials considered for review for this indicator were STEM projects. The instructional materials reviewed for Grade 4 do not meet the expectations for this indicator. The review team found that the instructional materials assess grade level content beyond the scope of the grade. The out of grade level standards assessed are not Mathematically reasonable for this grade level.

STEM materials that assess grade level content beyond Grade 4.

  • Rocket Apogee STEM Project on pages 71 – 94 of the teacher STEM project edition
    • This project asks students to find angle measurements of right triangles using the tangent ratio. While it is noted that this is above grade level, this is not to be addressed until high school according to HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles; and HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
    • This project asks students to identify outliers and calculate averages. These are not to be addressed until Grade 6 according to 6.SP.B.5.C.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
  • 3D GEO STEM project on pages 95 – 108 of the teacher STEM project edition
    This project recommends students use Euclidean construction for geometric structures. While it is noted that this is above grade level, this is not to be addressed until HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Review Team Note: A separate supplemental digital assessment database is available for an additional purchase cost. The review team did not analyze this supplemental digital assessment database as evidence for indicator 1a due to the fact that this additional component is not provided as part of the core 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 because the material did not spend the majority of time on the major clusters in the grade. There is little work on models and representations, and procedures are called for in situations that are more aligned to work in future grades. There was evidence found and cited where actual student activities do not align with the standards that are labeled in the materials and where students are engaging in work above 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 materials do not spend the majority of class time on the major cluster of each grade. A total of 72 activities/lessons are provided, and some may be repeated or take additional class periods. However, of the 72 activities/lessons, only 45 are aligned to major work of the grade, according to the table of contents. If the 45 lessons were fully aligned, 62.5% of the time is spent on the major work. Looking more closely, the percent of time spent on major work is below 62.5%. The lessons are labeled as aligned to major work of the grade, but the activities in the lessons do not actually align. Examples of this misalignment can be found in:

  • ART page 81, denominators of 60, and ART page 96, denominators of 36. These examples are not the denominators that should be present in the Grade 4 standards.
  • Pages 1-28 in ART do not fully align with the intent of the standards.
  • There is little work with multi-step problems, work is often single- and double-digit, and there is little interpretation of the multiplicative comparison.
  • The depth of work on OA.C.5 in pages 67-78 lacks connections to algebraic patterns.
  • On page 31, the standard 4.OA.A.2 is not supported with the question-and-answer format that is presented. The standard asks for students to solve problems within a word problem by showing their thinking through drawings and equations, but this page is simply rote memory format without asking students to demonstrate thinking through drawings or equations.
  • The standard 4.NBT.A.1 is not fully addressed with the lessons on pages 87-96. The lesson only briefly mentions that place value of a number is 10 times the place value to its right. The student work is identifying place value of numbers through multiple choice, matching numbers with their word form, and multiplying and dividing numbers by 10. There is no effort to connect that the place value is 10 times the place to the right in the number.
  • Only 12 of the 34 lessons in the student book adequately cover major clusters. The following are not adequately covered:
    • 4.OA.A.2 (pages 15-31). Only 2 problems use drawings.
    • 4.NBT.A.1 (pages 80-96). Half of the pages are identifying place value and half are multiplying and dividing by tens, neither of which is 4.NBT.A.1.
    • 4.NBT.A.3 (pages 117-141). Five of the student pages are estimating, not just rounding.
    • 4.NBT.B.5 (pages 160-179). These lessons use fluency for multiplication with larger numbers, a Grade 5 standard.
    • 4.NBT.B.6 (pages 180-203). These lessons use fluency for division with larger numbers, a Grade 6 standard.
    • 4.NF.B.4.A (pages 298-309). Not all the pages include pictures or models.
    • 4.NF.B.4.B (pages 310-319). These lessons are not based on any true understanding; they simply use a procedure with multiplication.
    • 4.NF.B.4.C (pages 327-328). The drawings are supposed to help students solve the problems but students are asked to draw the picture after getting an answer.
    • 4.NF.C.7 (pages 355-372). The lessons lack opportunities to have students give justification of conclusions/answers.

Because of these misalignments, the actual time spent on major work would be less than the amount of time noted according to the table of contents.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
0/8
+
-
Criterion Rating Details

The review team found that the coherence between the standards at the Grade 4 level fall short of meeting expectations for these criterion. Materials do not give students extensive work on grade level problems. Multiplication throughout all three resources is a rush to procedure and there is little development and understanding of place value and groups.

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 for supporting content reviewed for Grade 4 do not meet expectations. The following evidence exemplifies a lack of coherence between and among content standards.

  • The ART lesson on page 152 does not support the major work of 4.NF and there is a misrepresentation of a line plot.
  • The identification of factors does not support major work because it is out of context, both in teacher edition on page 48, and in the student edition on page 29.
  • The ART Lesson on page 19 does not meet standard and also seems forced content to connect with the Olympics (4.OA.B.4).
  • In the ART lesson on pages 136-139, there are no recording equivalents in a two-column table and there is no generating conversion table or listing number pairs (4.MD.A.1).
  • ART page 152 does not correctly utilize or represent a line plot (4.MD.B.4). The standard in this cluster requires students to use a line plot to display measurements in fractions of a unit and to solve problems involving addition and subtraction of fractions, connecting it directly to the 4.NF clusters.

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 for Grade 4 do not meet expectations for the amount of content designated for the year as viable for one school year in order to foster coherence between grades.

  • For instance, 4.OA.A should have lessons that allow for in-depth work. There are seven lessons between the three resources labeled with standards in 4.OA.A out of the 72 total lessons.
  • Beyond that, not all of these lessons are fully aligned to 4.OA.A. The STEM lesson "Plan your Escapement" has connections to 4.MD, which are not made and do not fully address interpretation of equations, multiplicative comparisons, and solving multi- step problems.
  • The STEM lesson "Rocket Apogee" has many instances of above grade-level work on tangent ratio, base distance and altitudes.

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 for Grade 4 do not meet expectations for consistency with the progressions in the standards. Evidence of denominators outside of the scope of Grade 4 are scattered throughout. For example:

  • ART page 81.
  • ART pages 90 and 96. The use of terms such as "improper fraction" and "reduce" are not consistent with the language in the progressions.

Additional evidence of pieces that lacked consistency with the progressions can be found on:

  • Teacher edition page 162 is the only example found for the use of arrays and the area model. This is not substantial enough to develop and explain understanding of this representation as way to solve multi-digit multiplication.
  • The STEM Lesson "3-D Geometry" is beyond the scope of Grade 4 mathematics.
  • Connections between unit fractions and addition of fractions and adding with the same denominators are not fully developed. These connections as well as the understanding of the size of the whole, from Grade 3, are missing in all three resources.
  • Teacher edition pages 234-297 rush to procedures and do not build on the conceptual understanding of fractions from Grade 3 standards.
  • The mathematical practices are not indicated nor aligned throughout lessons and instead are provided their own set of activities at the end of the book. This exact same set of activities appears in all teacher editions, Grades 3-5.

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 expectations for fostering coherence through connections at a single grade. Learning objectives are written and either address learning at the individual standard level or simply restate the cluster. In other instances the objectives are written as activities so say what the students will be doing, not what they will learn. For examples, see teacher edition, pages 333 and 434 and STEM page 2, "Plan your Escapement."

Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. There is no evidence of lessons/activities where standards exist across domains. For example, there are missing 4.NF and 4.MD connections, and 4.MD and 4.OA connections throughout the resources.

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: 2012

Title ISBN Edition Publisher Year
null 9781587807266 null null null
null 9781587807273 null null null
null 9781847008398 null null null
null 9781847008718 null null null
null 9781908018459 null null null
null 9781908018824 null null null

About Publishers Responses

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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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