Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 6 do not meet the expectations for alignment to the CCSSM. An exceptional aspect of the materials is the integrated nature of the lessons. No topic is taught in isolation. Major work is incorporated in to supporting topics and many connections are made between domains and clusters. The materials go to great lengths to develop a conceptual understanding of math topics. However, the materials frequently cover off grade-level topics. In doing this only approximately 50 percent of the time is spent on the major work of the grade. The materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade level concepts explicitly to prior knowledge, and the lesson objectives are not shaped by the CCSSM cluster headings. Since the materials do not meet expectations for focus and coherence in Gateway 1, they were not reviewed for evidence of rigor and the mathematical practices in Gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
5
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 6 do not meet the expectation for focus and coherence with the CCSSM. Some included assessment items are above grade-level. Major work topics only account for approximately 50 percent of the instructional time. Major work is incorporated into lessons that focus on the supporting work, however too many topics are off grade-level. The integrated nature of the materials gives ample opportunity for supporting work to enhance the major work, and there are also many connections made between domains and clusters. However, far too much time is spent covering off grade-level topics. Because of this, the amount of content for one grade level is not viable for one school year. Furthermore, the materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade level concepts explicitly to prior knowledge, and the materials are not shaped by the CCSSM cluster headings.

Criterion 1a

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

The instructional materials reviewed for Grade 6 meet the expectations for assessing material at the Grade 6 level. There are a few concepts assessed that are beyond the Grade 6 CCSSM, but the alteration or omission of these items would not significantly impact the structure of the materials. Overall, to avoid including topics that are above grade-level some modification of the materials would need to be made, but there are not enough above-grade level assessment questions to say that the materials would be significantly impacted by such an alteration.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectations for assessment. There are only a few above grade-level assessment items whose accompanying lessons cannot be modified without impacting the underlying structure of the instructional materials. The instructional materials offer assessment materials on their Flourish website. These assessment materials include a quiz for each section of a unit and a unit test. There is an included test generator, which would enable teachers to omit all above grade-level assessment items. For this reason, when above grade-level questions were found on the unit tests and quizzes, the corresponding sections were examined to see the extent that students would be expected to understand the above grade-level topics and if it would be possible to modify the lesson. Listed below are the above grade-level assessment items that cannot be modified without impacting the structure of the materials and above grade-level assessment items that could be easily omitted without impact to the materials.

Assessment Items that impact the materials:

  • At this Rate, Question 13: In this question, students are told to find x in the proportion. Proportions are not included in the Grade 6 CCSSM. In Lesson 1.2, there is an effort made to explain proportions in terms of equivalent ratios with scaling up and scaling down, much in the way one would write equivalent fractions. However, in the subsequent lessons in Section 1, the use of proportions are included throughout the lessons. In the teacher materials there is a note that states that the methods involve proportions, but students may use other methods, but those methods are not spelled out in the student or teachers materials.
  • A Balancing Act, Unit Test Questions 20, 21 and 23d: These involve students writing a rule in the form px + q = r. This is 7.EE.4.A. This topic is included in Lesson 1.3 and incorporated into subsequent lessons.
  • A Balancing Act, Unit Test Question 9: This question has students solve a system of equations, which aligns to 8.EE.8. The materials show students how to solve a problem of this type by using a guess, check and refine method, as well as a substitution method. Regardless of the method, it is still an above grade-level topic that is incorporated into lesson 2.2.

Above grade-level assessment items that could be skipped without impacting the materials:

  • A Balancing Act, Unit Test Question 23b and c: Students are supposed to interpret points and lines for two displays of data on a graph to answer questions about linear relationships, which aligns to the cluster 8.EE.B. This topic is in Lesson 3.5, the last lesson of the unit, and could be omitted from the test.

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 6 are not developed so that students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. Approximately 50 percent of the days are spent on the major work of the grade, while the supporting work does incorporate some major work, too much time is spent on off grade-level topics. Overall the instructional materials do not meet the criteria for the time devoted to the major work of the grade.

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 6 do not meet the expectations for focus by spending a majority of class time on the major clusters of the grade. There are five books/units included in the Grade 6 materials, those five books/units are each divided into three sections, which are then divided into lessons. A pacing guide is provided, which breaks down the number of days (45-minute class periods) per lesson. To determine the amount of time spent on major work, three perspectives were evaluated: 1) the number of sections devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days devoted to major work is the most accurate reflection for this indicator because it specifically addresses the amount of class time spent on concepts. Overall, 62 out of the 123 days (approximately 50 percent) of class time is devoted to major work, 25 out of 123 days (approximately 20 percent) of class time is devoted to supporting work, and 36 out of 123 days (29 percent) is spent covering off grade-level topics. At times, some lessons included major or supporting clusters and included above/below level work, and in those cases, the time was divided based on the number of examples and problems.

  • A Balancing Act: (20.5 out of 27 days of major work. 6.5 days off grade-level work.)
  • Section 1: (7 out of 7 days on major work.)
    • Lesson 1: Primarily covers 6.EE.B (2 days of major work.)
    • Lesson 2: Primarily covers 6.EE.A and 6.EE.B (2 days of major work.)
    • Lesson 3: Primarily covers 6.EE.B (2 days of major work.)
    • Lesson 4: Primarily covers 6.EE.A, 6.EE.B (1 day of major work.)
  • Section 2: (8.5 out of 11 days on major work. 2.5 days off grade-level.)
    • Lesson 1: Primarily covers 6.EE.A (2 days of major work.)
    • Lesson 2: Primarily covers 6.EE.A and above grade-level work 8.EE.C (1 day of major work. 1 day off grade-level.)
    • Lesson 3: Primarily covers 6.EE.A (4 days of major work.)
    • Lesson 4: Primarily covers 6.EE.B and above grade-level work 7.EE.B (0.5 days of major work. 0.5 days off grade-level.)
    • Lesson 5: Primarily covers 6.EE.B and above grade-level work 7.EE.B (1 day of major work. 1 day off grade-level.)
  • Section 3: (5 out of 9 days on major work. 4 days off grade-level.)
    • Lesson 1: Primarily covers 6.EE.A (1 day of major work.)
    • Lesson 2: Primarily covers 6.EE.A and 6.EE.B (2 days of major work.)
    • Lesson 3: Primarily covers above grade-level work F.BF.A.1.A (2 day off grade-level.)
    • Lesson 4: Primarily covers 6.EE.C (2 days of major work.)
    • Lesson 5: Primarily covers above grade-level work 8.EE.B (2 days off grade-level.)
  • At This Rate: (14.5 out of 22 days of major work. 6 days of supporting clusters. 1.5 days off grade-level work)
  • Section 1: (12 out of 12 days on major work)
    • Lesson 1: Primarily covers 6.RP.A (3 days of major work.)
    • Lesson 2: Primarily covers 6.RP.A (3 days of major work.)
    • Lesson 3: Primarily covers 6.RP.A (1 day of major work.)
    • Lesson 4: Primarily covers 6.RP.A (1 days of major work.)
    • Lesson 5: Primarily covers 6.RP.A (2 days of major work.)
    • Lesson 6: Primarily covers 6.RP.A (2 days of major work.)
  • Section 2: (1.5 out of 3 days of major work. 1.5 days off grade-level.)
    • Lesson 1: Primarily covers 6.RP.A (1 day of major work.)
    • Lesson 2: Primarily covers 6.RP.A and 6.EE.C and above grade-level work 7.RP.A (0.5 day of major work. 0.5 day off grade-level.)
    • Lesson 3: Primarily covers above grade-level work 7.RP.A and 8.SP.A (1 day off grade-level.)
  • Section 3: (1 out of 7 days of major work. 6 days of supporting clusters.)
    • Lesson 1: Primarily covers 6.SP.A and 6.SP.B (2 days of supporting clusters.)
    • Lesson 2: Primarily covers 6.SP.A and 6.SP.B (1 day of supporting clusters.)
    • Lesson 3: Primarily covers 6.SP.A, 6.SP.B, and 6.NS.C (1 day of major work. 1 day of supporting clusters.)
    • Lesson 4: Primarily covers 6.SP.A and 6.SP.B (2 days of supporting clusters.)
  • Fraction Times: (8 out of 27 days on major work. 8 days of supporting clusters. 11 days off grade-level.)
  • Section 1:( 2.5 out of 11 days on major work. 0.5 days of supporting clusters. 8 days off grade-level.)
    • Lesson 1: Primarily covers 6.EE.A and below grade-level work 5.NF.B (1 day of major work. 1 day off grade-level)
    • Lesson 2: Primarily covers below grade-level work 5.NF.B (2 days off grade-level.)
    • Lesson 3: Primarily covers below grade-level work 5.NF.B (3 days off grade-level.)
    • Lesson 4: Primarily covers some 6.NS.B and 6.EE.A but includes below grade-level work 5.NF.B (0.5 days of major work. 0.5 days of supporting clusters. 1 day of off grade-level.)
    • Lesson 5: Primarily covers 6.EE.A and below grade-level work 5.NF.B (1 day of major work. 1 day off grade-level)
  • Section 2: (5 out of 8 days of major work. 3 days off grade-level)
    • Lesson 1: Primarily covers below grade-level work 5.NF.B (2 days off grade-level.)
    • Lesson 2: Primarily covers 6.NS.A and below grade-level work 5.NF.B (1 day of major work. 1 day off grade-level.)
    • Lesson 3: Primarily covers 6.NS.A (2 days of major work.)
    • Lesson 4: Primarily covers 6.NS.A (2 days of major work.)
  • Section 3: (0.5 out of 8 days of major work. 7.5 days of supporting clusters)
    • Lesson 1: Primarily covers 6.NS.B (2 days of supporting clusters.)
    • Lesson 2: Primarily covers 6.NS.B and 6.EE.3 (0.5 days of major work. 0.5 days of supporting clusters.)
    • Lesson 3: Primarily covers 6.NS.B (1 day of supporting clusters.)
    • Lesson 4: Primarily covers 6.NS.B (2 days of supporting clusters.)
    • Lesson 5: Primarily covers 6.NS.B (2 days of supporting clusters.)
  • Notable Numbers: (6 out of 21 days on major work. 6 days of supporting clusters. 9 days off grade-level.)
  • Section 1: (6 out of 9 days of major work. 2 days of supporting clusters. 1 day off grade-level.)
    • Lesson 1: Primarily covers 6.RP.A (1 day of major work.)
    • Lesson 2: Primarily covers 6.RP.A (2 days of major work.)
    • Lesson 3: Primarily covers 6.RP.A (1 day of major work.)
    • Lesson 4: Primarily covers 6.RP.A (1 day of major work.)
    • Lesson 5: Primarily covers 6.NS.B (2 days of supporting clusters.)
    • Lesson 6: Primarily covers below grade-level work 5.NF.B and 4.NF.A (1 day off grade-level work.)
    • Lesson 7: Primarily covers 6.RP.A (1 day of major work.)
  • Section 2: (0 out of 3 days of major work. 3 days off grade level.)
    • Lesson 1: Primarily covers below grade-level work 4.NF.A and 5.NBT.A (0 days of major work.)
    • Lesson 2: Primarily covers below grade-level work 4.NF.A and 5.NBT.A (0 days of major work.)
    • Lesson 3: Primarily covers below grade-level work 4.MD.A and 5.MD.A (0 days of major work.)
  • Section 3: (0 out of 9 days of major work. 4 days of supporting clusters. 5 days off grade-level.)
    • Lesson 1: Primarily covers below grade-level work 5.NF.A (2 days off grade-level.)
    • Lesson 2: Primarily covers below grade-level work 5.NF.A (1 day off grade-level.)
    • Lesson 3: Primarily covers 6.NS.B (2 days of supporting clusters.)
    • Lesson 4: Primarily covers 6.NS.B (1 day of supporting clusters.)
    • Lesson 5: Primarily covers below grade-level work 5.NF.A (2 days off grade-level.)
    • Lesson 6: Primarily covers 6.NS.B (1 day of supporting clusters.)
  • Sizing Up Shapes: (13 out of 26 days on major work. 5 days of supporting clusters. 8 days off grade-level.)
  • Section 1: (0 out of 8 days on major work. 8 days off grade level.)
    • Lesson 1: Primarily covers below grade-level work 5.G.B (2 days off grade-level.)
    • Lesson 2: Primarily covers below grade-level work 5.G.B and 4.G.1 (1 day off grade-level.)
    • Lesson 3: Primarily covers below grade-level work 5.G.B (1 day off grade-level.)
    • Lesson 4: Primarily covers below grade-level work 5.G.B (2 days off grade-level.)
    • Lesson 5: Primarily covers below grade-level work 5.G.B (2 days off grade-level.)
  • Section 2:( 8 out of 8 days on major work.)
    • Lesson 1: Primarily covers 6.NS.C (2 days of major work.)
    • Lesson 2: Primarily covers 6.NS.C (3 days of major work.)
    • Lesson 3: Primarily covers 6.NS.C (1 day of major work.)
    • Lesson 4: Primarily covers 6.NS.C (2 days of major work.)
  • Section 3: (5 out of 10 days of major work. 5 out of 10 days of supporting clusters.)
    • Lesson 1: Covers 6.G.A, 6.EE.A and 6.EE.B (1 day of major work. 1 day of supporting clusters.)
    • Lesson 2: Covers 6.G.A, 6.EE.A and 6.EE.B (0.5 days of major work and 0.5 days of supporting clusters.)
    • Lesson 3: Covers 6.G.A, 6.EE.A and 6.EE.B (1.5 days of major work and 1.5 days of supporting clusters.)
    • Lesson 4: Covers 6.G.A, 6.EE.A and 6.EE.B (1 day of major work and 1 day of supporting clusters.)
    • Lesson 5: Covers 6.G.A, 6.EE.A and 6.EE.B (1 day of major work and 1 day of supporting clusters.)

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
3/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectations for being coherent and consistent within the standards. The integrated nature of the materials gives ample opportunity for supporting work to enhance the major work, and there are also many connections made between domains and clusters. However, far too much time is spent covering off grade-level topics. Because of this, the amount of content for one grade level is not viable for one school year. Furthermore, the materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade level concepts explicitly to prior knowledge, and the materials are not shaped by the CCSSM cluster headings.

Indicator 1c

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

The instructional materials reviewed for Grade 6 meet the expectation for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. It is noted that the theme of the materials is to integrate several topics into one lesson and as a result no one topic is taught in isolation. Overall, the major work of Grade 6 is incorporated into lessons that focus on the supporting clusters, and some examples of this indicator are listed below.

  • Sizing Up Shapes:
    • Lessons 3.1, 3.2, and 3.3. Students develop an understanding and apply the measurements of quadrilaterals and triangles (6.G.1). In doing this, students simultaneously develop and apply formulas for perimeter and area of these shapes. Thus, they are also practicing using expressions that arise from formulas used in real-world problems (6.EE.2.C).
    • Lesson 3.5. Students determine the volume of rectangular prisms (6.G.2). In the On your Own section, the students are given various dimensions and told to solve for an unknown dimension. Therefore, students are setting up and solving equations (6.EE.7).
  • At This Rate:
    • Lesson 3.3. By learning about mean and mean absolute deviation (6.SP.3), students continue to develop and practice their knowledge of absolute value (6.NS.7.C).
  • Fraction Times:
    • Lessons 1.4 and 2.2. Students practice multiplying mixed numbers (6.NS.3). The materials have students do this by using area models (6.G.1) to develop an understanding of the distributive property (6.EE.3).

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 6 do not meet the expectations for the amount of content designated being viable for one school year. The materials are designed for approximately 177 days of instruction, which includes: days spent on the lessons in the student editions, time spent reviewing and taking quizzes and tests, and time spent on projects and interactive whiteboard activities. However, there are many off grade-level concepts covered in that time frame, and some of the Grade 6 standards are not fully attended to.

  • The instructional materials would take approximately 177 days to cover, however much time is spent on off grade-level work. If a teacher skipped these topics, that removes about 51 days of work, taking the amount of time to 126 days.
  • The materials do cover the major work of the grade. However, the supporting clusters 6.NS.B are not covered to the full intent of the standards.
    • The materials claim to cover 6.NS.2 in section 1.6 of Notable Numbers, but there is very little evidence of students using the standard algorithm to divide multi-digit whole numbers. The materials also claim to cover this in Fraction Times sections 3.4 and 3.5, but these sections are devoted to dividing decimals.
    • The chapters aligned to 6.NS.3 build a conceptual understanding of operations with decimals and making connections to fractions. Conceptual understanding is largely built in earlier grades. The expectation of 6.NS.3 is for students to gain fluency using the standard algorithm for each operation. The materials provide very little practice using the standard algorithm, and as presented, students will not gain fluency and be prepared for the next grades.
    • When it comes to 6.NS.4, the concepts of greatest common factor (GCF) and least common multiple (LCM) are covered but not in the way stated in the standard. In the materials, GCF and LCM are used to work with fractions as seen in Notable Numbers section 1.5 where students use the GCF to simplify fractions and the LCM to add and subtract fractions. However, they are not incorporated into using the distributive property to write two equivalent expressions as required by the standard and progressions.

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 6 do not meet the expectation for having materials that are coherent and consistent with the standards. Materials attempt to follow grade-by-grade progressions, however too much attention is given to off grade-level standards. Materials do not give all students extensive work with grade-level problems, and grade-level concepts are not explicitly related to prior knowledge.

Materials do not develop according to the grade-by-grade progressions in the standards. Content from prior or future grades is not clearly identified and related to grade-level work.

  • When there is content from prior or future grades, the content is not clearly identified and not explicitly stated. Some of the materials attempt to relate to prior knowledge by addressing below, grade-level standards, but this is not explicitly stated.
  • Off, grade-level work is present in every book/unit. The off grade-level work is not identified as such, though in some cases it might be a plausible extension or reinforcement of grade-level standards. In many cases, it is deliberately teaching a topic that is not intended in the Grade 6 standards. For example, in section 2 of Notable Numbers, the materials claim to align to 6.NS.3, 6.NS.4, 6.NS.6, 6.NS.7 and 6.RP.3. However, the main focus of the lessons in these sections is comparing and ordering positive fractions and decimals on a number line, which are below grade-level topics. At times, there are problems or examples that may touch upon the grade-level standards, however, there is no indication in the materials when this is happening.
  • The notes in the Teachers’ Edition at the start of each section, “Teaching the Lesson,” attempt to explain what concepts need to be developed first before they are able to be successful in the grade-level concepts and even above-level concepts. The progressions with the concepts are somewhat explained here, yet, it does not identify any standards within the unit.
  • There is evidence that the materials are following the progressions. However, they are not necessarily concentrating on the mathematics of the grade. For example, in the book/unit Fraction Times, the first two sections are dedicated to the goal of dividing fractions. In section 1, lesson 1 multiplies fractions to a whole number; lesson 2 multiplies a fraction to a fraction; lesson 3 further multiplies fractions and whole numbers; lesson 4 multiplies mixed numbers; and lesson 5 estimates products of fractions. In section 2, lesson 1 involves dividing a fraction by a whole number, and the last three lessons in section 2 focus on dividing a fraction by a fraction. 6.NS.A does state to apply and extend the previous understanding of multiplication and division to dividing a fraction by a fraction, and extending this understanding involves making the connection that division is the inverse of multiplication. At times some grade-level concepts, like distributive property and area are incorporated, but the clear goal is to reteach multiplying fractions. This unit is following the progressions, in that it reteaches below grade-level concepts that lead to dividing a fraction by a fraction. However, these are progressions that are covered in elementary grades, the overall focus of this standard is lost in the amount of review.

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

  • The problems in the On Your Own section provide students with the opportunities to engage deeply with the mathematics. The problem sets begin with writing about mathematics. The problem structures focus on open-ended, thought-provoking questions in which a student frequently has to perform an investigation and justify their reasoning.
  • The materials do not designate specific problems and examples that are on grade level as being appropriate for struggling students. It is expected that all students will engage in most of the problems. There are some suggested teaching strategies and tips, and some ready-made tools to help with special populations. However, if a student is not able to keep up with the high-level questions provided in the On Your Own section of the student materials, no alternates are provided.
  • For advanced students, there are Think Beyond Questions that are more rigorous and involve topics from later grades, and these can be found at the end of the On Your Own sections and can be included at the teacher discretion.

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

  • There are no signals or indications of when something is review or new information. The lessons frequently contain topics that are presented in a way that span multiple grade levels. However, the materials provide no indication of when this is happening and only indicate which grade-level topic is present. Furthermore, because of the integrated nature of the materials, even when a multi-grade topic is covered, it is almost impossible to easily identify the on-grade portion of the lesson.
  • The connections between concepts from previous grade levels are not clearly articulated from lesson to lesson. They make an effort to explain this process in the "Goals of the Unit" summary, but they do not clearly identify previous grade level standards to the current grade level standards.

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 6 partially meet the expectation to foster coherence through connections at a single grade, where appropriate and required by the standards. The very integrated nature of the materials leads to frequent domain-to-domain and cluster-to-cluster connections. However, the materials partially have learning objectives that are shaped by the CCSSM. Overall, the materials included lessons that are not presented in isolation of other important topics, but the materials are not shaped by the CCSSM alone.

Materials partially include learning objectives that are visibly shaped by CCSSM cluster headings.

  • There are clearly identified lesson objectives at the beginning of each lesson that describe what students should be able to do by the end of the lesson. The problem is that many of the objectives are not at grade level nor is there any indication that they are visibly shaped by CCSSM cluster headings. For example, in lessons 1:1-1:5 of “Sizing Up Shapes,” the publishers claim to be addressing Grade 6 clusters related to the CCCSM (6.G.A.1 and 6.G.A.2). In reality, these lessons are based on Grade 5 standards with classifying polygons based on their size and shapes. There seems to be a disconnect between the cluster headings stated by the publisher and the actual clusters within certain lessons.
  • There are five books/units included in the materials. These books/units seemingly cover a CCSSM domain. Listed in the front of the books/units of the teacher materials is a section that states the alignment to the CCSSM. However, one of the books, A Balancing Act, omits this section. Even though some of the lessons are aligned to the CCSSM, the materials do not solely follow the CCSSM standards and cluster headings.

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.

  • The materials are very integrated, and as a result, there are numerous examples of places that connections are made between domains and clusters. Some of those examples are explained below.
    • Sizing Up Shapes, lesson 2.2: In this lesson, students are expected to practice graphing numbers on the coordinate plane. (6.NS.6 and 6.NS.8). Integrated into this lesson are several examples where students are drawing and analyzing polygons (6.G.3).
    • Fraction Times, lesson 3.2: In this lesson, students practice multiplying mixed decimals (6.NS.B). The materials have students do this by using area models (6.G.1) to develop an understanding of distributive property (6.EE.3).
    • A Balancing Act, lesson 1.2: In this lesson, students analyze properties of operations and use variables to write expression (6.EE.A). This leads student to writing equivalent expressions and then solving for the variable (6.EE.B).

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 Apr 08 00:00:00 UTC 2016

Report Edition: 2013

Title ISBN Edition Publisher Year
null 978-0-7575-6212-9 null null null
null 978-0-7575-6213-6 null null null
null 978-0-7575-6685-1 null null null
null 978-0-7575-6686-8 null null null
null 978-0-7575-6702-5 null null null
null 978-0-7575-6703-2 null null null
null 978-1-4652-1232-0 null null null
null 978-1-4652-1243-4 null null null
null 978-1-4652-1256-6 null null null
null 978-1-4652-1258-0 null null null

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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