Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 6 do not meet the expectation for alignment to the CCSSM. The materials partially meet expectations in the areas of focus and coherence, but they do not meet the expectations in the areas of rigor and the MPs. In the area of focus within the grade, some above grade-level questions are included on the assessments but a teacher could modify the lessons without impacting the structure of the materials. The materials are not designed to devote the majority of class time to the major work of the grade. In the area of coherence, the materials include content that is shaped by the CCSSM clusters with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems with supporting and additional content that engages students in the major work of the grade. Natural connections are made between clusters and domains. However, the materials fail to note grade to grade progression.

In the area of rigor and balance, though all three aspects of rigor are present in the materials, they are often presented separate from each other and not used in a balanced way to develop a concept. The inquiry labs are used to develop conceptual understanding, however, the concepts developed in the inquiry labs are not referenced in the lessons. There is an abundance of procedural skills, but without solid work at conceptual understanding, students are left to memorize procedures. The application problems presented in the materials often tell students how to solve the problem with only limited opportunities for students to find their own solution path. In the area of practice content connections, the materials attempt to incorporate the MPs in each lesson. However, the materials are so frequently labeled as MPs that a teacher cannot reliably use the materials to know when MPs are being carefully attended to. There are many instances when questions are labeled as an MP, but in fact, they are just a computation question. The materials incorporate questions in which students have to justify and explain their answers, but lack lesson structures in which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented but not always incorporated meaningfully into the lesson.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
8
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
7
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

Partially Meets Expectations

+
-
Gateway One Details

The materials reviewed for the Grade 6 partially meet the expectations for focus and coherence with the CCSSM. The materials are shaped by the CCSSM, but the materials lack focus.The materials do not spend the majority of class time on the major clusters for Grade 6. Even though the materials include assessment materials that are above grade level, those items could be skipped or modified without impacting the structure of the materials. There are aspects of coherence in the materials that are exceptional. However, there is a lack of clear grade-to-grade progressions, and some missed opportunities for Grade 6 domain to domain connections.

Criterion 1a

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

The instructional materials reviewed for Grade 6 assess some topics that are above grade-level. However, the affected assessments and their accompanying lessons can be modified or skipped without impacting the underlying structure of the instructional materials. Moreover, there is a variety of included assessment types that cover all of the CCSSM. Overall the instructional materials meet the expectation for focus within assessment.

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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectation for assessment because above grade-level assessment items, and their accompanying lessons, can be modified or omitted without significantly impacting the underlying structure of the instructional materials. For this indicator, the four quarterly benchmark tests were reviewed first, then for a more in-depth look at each CCSSM indicator, the chapter tests, extended response tests, and performance tasks were examined.

  • The instructional materials offer multiple tiers of assessment on their ConnectEd website.These include pretests, diagnostic tests, chapter quizzes, chapter tests, performance tasks, extended response tests, quarterly benchmark tests, standardized test practice as well as SBAC and PARCC practice test questions. Furthermore, a test generator is included so that educators can create their own assessments to suit their needs.
  • The first quarterly benchmark test assesses the following Grade 6 standards: 6.RP.1, 6.RP.2, 6.RP.3, 6.NS.2, 6.NS.3, and 6.NS.4. These standards are primarily covered in chapters 1-3. The listed CCSSM are covered on the assessments with no above grade-level items.
  • The second quarterly benchmark test assesses the following Grade 6 standards: 6.NS.1, 6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8, 6.EE.1, 6.EE.2, 6.EE.3, and 6.EE.4. These standards are primarily covered in chapters 4-6. All of the listed CCSSM are covered on the assessments. The second quarterly benchmark test has two above grade-level questions on it. Question 1 is a story problem that uses the concept of scale models. For a student to understand the problem they would have to understand the concept of scale. According to the CCSSM, scale is presented in Grade 7. (7.G.1 - Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.) None of the corresponding chapter tests, extended response tests, or performance tasks used scale in their questions, thus no points were deducted. Questions 13 and 18 involve converting a fraction into a decimal. According to the CCSSM this is Grade 7 standard. (7.NS.2.D - Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.) On the corresponding chapter test, the first four question involve this concept. These questions stem from chapter 5, lesson 4 and if this lesson were skipped, lesson 5 would also have to be skipped because that lesson requires students to convert fractions to decimals using long division. This problem could be overcome if the two affected lessons were skipped, and a teacher used the included test generator to create a new chapter test.
  • The third quarterly benchmark test assesses some of the previously covered standards and 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9, 6.G.1 and 6.G.3. These standards are primarily covered in chapters 7-9. All of the listed CCSSM are covered on the assessments. There is above grade-level vocabulary used in various places on the benchmark and chapter tests. Questions 10, 11 and 20 on the third quarter benchmark test make references to the word and definition of "function." In the CCSSM functions are not introduced until Grade 8. These questions stem from Chapter 8 "Functions and Inequalities" and are also included on the chapter tests. Even though the word functions is used at this grade level, it was determined that this did not represent a significant impact on the structure of the materials because the lessons and assessments keep very true to the intent of the Grade 6 CCSSM. The listed Grade 6 standards will lead students to an understanding of functions in Grade 8; however, including the word "functions" in Grade 6 before students have a true understanding of its meaning is unnecessary.
  • The end of year benchmark test assesses some of the previously covered standards and 6.G.2, 6.G.4, 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4 and 6.SP.5. These standards are primarily covered in chapter 10-12. All of the listed CCSSM are covered on the assessments with no new above grade-level items.

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 do not meet the expectations for spending the majority of class time on major work. The materials spend approximately 56 percent of the instructional time on the major clusters. Even though the non-major clusters incorporate some major work, the amount of time spent on off grade level topics takes away from the time spent on major work. Overall, the materials do not spend enough time focused on 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. To determine this, three perspectives were evaluated: 1) the number of chapters 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 a true reflection for this indicator because it specifically addresses the amount of class time spent on concepts. Overall, the materials spend 56 percent of instructional time on the major clusters of the grade. The Grade 6 materials have 12 chapters that contain 79 lessons. (The inquiry labs were considered as part of the lesson that they supported.) A total of 159 days (optional projects not included) of class time was scheduled for the lessons.

  • Five out of 12 chapters (42 percent) focus exclusively on the major clusters of Grade 6, while the other seven chapters have a mix of off, grade-level work and non-major clusters.
  • Each chapter is made up of lessons. When examining the individual lessons, 49 percent of class time is spent on the major clusters of the grade. The lesson breakdown is as follows:
    • Chapter 1 has seven lessons: Lessons 2 – 7 focus on the major clusters (6.RP.1, 6.RP.2, and 6.RP.3), while lesson 1 covers non-major cluster (6.NS.4). Six out of seven lessons in chapter 1 are on major work.
    • Chapter 2 has eight lessons: Lessons 1 – 5 are considered off grade level, they are listed as preparation for 6.RP.3.C. Lessons 6 – 8 focus on major clusters (6.RP.3). Three out of 8 lessons in chapter 2 are on major work.
    • Chapter 3: Eight out of eight lessons are on non-major clusters (6.NS.2 and 6.NS.3).
    • Chapter 4 has eight lessons: Lessons 1 - 4 are considered off grade-level, they are listed as preparation for 6.NS.1. Lessons 5 – 8 focus on major clusters (6.NS.1 and 6.RP.3). Four out of eight lessons in chapter 4 are on major work.
    • Chapter 5: Six out of seven lessons are on the major clusters (6.NS.5, 6.NS.6, 6.NS.7, and 8). Lesson 4 is an above grade level topic. Six out of seven lessons in chapter 5 are considered major work.
    • Chapter 6: Seven out of seven lessons are on the major clusters (6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.6).
    • Chapter 7: Five out of five lessons are on the major clusters (6.EE.5, 6.EE.7 and 6.RP.3).
    • Chapter 8: Seven out of seven lessons are on the major clusters (6.EE.2, 6.EE.5, 6.EE.6, 6.EE.8, and 6.EE.9).
    • Chapter 9 has six lessons: Lessons 1, 2, 3, 4 and 6 are considered supporting clusters (6.G.1, and 6.G.3). Lesson 5 is considered a major cluster (6.NS.8). One out of six lessons are considered major work.
    • Chapter 10: Five out of five lessons are considered supporting clusters (6.G.2 and 6.G.4)
    • Chapter 11: Five out of five lessons are considered additional clusters (6.SP.1, 6.SP.3, and 6.SP.5)
    • Chapter 12: Six out of six lessons are considered additional clusters (6.SP.2, 6.SP.4, and 6.SP.5)
  • A pacing guide is provided with the materials and gives the number of days each chapter and lesson should take, assuming that students have a solid understanding of the past years CCSSM, the pacing guide is accurate. When calculating the number of days, 56 percent of the class time is spent on the major clusters, 37 percent of the class time is spent on non-major clusters. The majority of the remainder of the class time is spent on below grade-level work. The breakdown of the number of days spent on the major cluster of the grade are as follows:
    • Chapter 1: Seven lessons should take 14 days, and 6 of the lessons are major clusters, which should take approximately 13 days.
    • Chapter 2: Eight lessons should take 14 days. Three of the lessons are major clusters, which should take approximately 8 days.
    • Chapter 3: Eight lessons should take 14 days. All of the lessons are non-major clusters.
    • Chapter 4: Eight lessons should take 14 days. Four of the lessons are major clusters, which should take approximately 10 days.
    • Chapter 5: Seven lessons should take 14 days. Six of the lessons are major clusters, which should take approximately 13 days.
    • Chapter 6: Seven lessons should take 15 days. All lessons are major clusters.
    • Chapter 7: Five lessons should take 12 days. All lessons are major clusters
    • Chapter 8: Seven lessons should take 13 days. All lessons are major clusters
    • Chapter 9: Six lessons should take 14 days. All of the lessons are supporting clusters, however, Lessons 2 and 3, students are expected to find a missing dimension in area problems. Therefore, students are practicing 6.EE.7. Additionally, Lesson 5 is a major cluster. Thus, 3.5 days are dedicated to major work.
    • Chapter 10: Five lessons should take 12 days. However, in Lessons 1 and 2, students are expected to find the missing dimension in volume of prisms problems, therefore, students are practicing 6.EE.7. Thus, 2 days are dedicated to major work.
    • Chapter 11: Five lessons should take 11 days. All of the lessons are non-major clusters.
    • Chapter 12: Six lessons should take 12 days. All of the lessons are non-major clusters.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for being coherent and consistent with the standards. The materials include content that is shaped by the CCSSM clusters with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems and non-major content engages students in the major work of the grade. The materials fail to note grade-to-grade progressions, and some natural connections between domains are missed.

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 meets the expectation for the non-major content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the lessons that focus on non-major content also engage students in major work where natural and appropriate.

In Chapter 9, Lessons 2, 3 and 4,and Chapter 10, Lessons 3, 4 and 5, students use formulas to find area in real-world problems. In doing this, students are simultaneously learning the non-major standard 6.G.1 and using the standard 6.EE.2.C.

In Chapter 10 Lesson 1, students use formulas to find the volume of rectangular prisms in real-world problems. Therefore, students are simultaneously connecting the non-major standard 6.G.2 to the major standard 6.EE.2.C.

In Chapter 9, Lessons 2 and 3, students are expected to find a missing dimension for parallelograms and triangles when the area of the figure is known. Therefore, students are simultaneously practicing the non-major work of 6.G.1 and the major work of 6.EE.7.

In Chapter 10, lesson 2, students are expected to find the missing dimension of rectangular prisms when the volume is known. Therefore, students are simultaneously practicing the non-major work of 6.G.2 and the major work of 6.EE.7.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meets the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The instructional materials are designed to take 159 – 169 days. Many additional resources can be found on the accompanying website. Overall, the amount of content that is designated for this grade level is viable for one school year.

  • Included in the materials is a yearlong pacing guide assuming that students have a solid understanding of the past years CCSSM, the pacing guide is accurate. According to that pacing guide, completing the work in the student edition would take 159 days. That includes time for a chapter opener, a mid-chapter quiz, a chapter review, and a chapter test. Ten extra days could be spent on the five unit projects.
  • There are areas where above and below grade-level topics are included in the materials. However, the Grade 6 CCSSM are developed to give students the practice they need to be prepared for Grade 7.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for the materials to be consistent with the progressions in the standards. The materials give all students extensive work on grade-level problems. Content from prior and future grades is identified but not explicitly stated. The materials attempt to relate grade-level problems to prior knowledge, but they fail to mention grade-to-grade progressions. Overall, the instructional materials partially meet the expectation to be consistent with the progressions in the standards.

  • The materials do an excellent job of giving all ability levels an opportunity for learning grade-level standards. The materials provide exercises for all levels of complexity and recommended homework options that are organized for students who are approaching, on level, or beyond level. The materials connect classwork to the homework assignments for all ability levels. For example, the materials use a variety of practice with “Power Up” activities for performance task problems and common core test practice for a challenging review structure. The materials suggests that students from all 3 levels are encouraged to try these higher order thinking problems, so students who need interventions still get to engage with the full depth of the grade-level standards.
  • Below grade-level work is listed as preparation for a standard. For example, chapter 2, lesson 3 is listed as preparation for 6.RP.3.C. The topic, percents and decimals, is connected to 6.RP.3.A. However, there is no mention of the grade that percents and decimals is taught in. Knowing the grade-level of this lesson might help a teacher adjust the pacing of the lesson and the ones that follow.
  • Lessons that are above grade-level are identified as extensions. For example. chapter 10, lesson 2 is labeled as an extension of 6.G.2. The topic of this lesson, finding the volume of a triangular prism, is an extension of the standard, and therefore it is correctly identified.
  • One lesson is incorrectly identified: Chapter 5, lesson 4 is listed as preparation for 6.NS.6.C and 6.NS.7.A. What is presented in this lesson is 7.NS.2.D. This is above grade level work that is not labeled as such. This lesson would more appropriately be labeled as an extension of the standard.
  • In the teacher edition a graphic is presented under coherence. It shows, "Previous, Now and Next." "Previous" lists what topics students learned that lead up to the current topic. "Now" lists what topics the students are learning now. "Next" lists what related topics the students will be learning. Although there is an attempt to be Coherent across the grade levels, there are no references to other grades' standards within the lessons.
  • The materials successfully integrate the Grade 6 CCSSM that state “apply and extend” past knowledge to current learning. (6.NS.A - Apply and extend previous understandings of multiplication and division to divide fractions by fractions.) In the chapter 4 inquiry lab and lesson 7, students check their division of fraction problems with multiplication. (6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.) In chapter 5, students extend their knowledge of whole numbers to include integers and rational numbers. (6.EE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.) In chapter 6, the lessons make a nice progression to ensure this connection. In lesson 2, students write and solve numerical expressions. In lesson 3, students evaluate algebraic expressions, and in lesson 4 students write algebraic expressions.

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 expectations for fostering coherence through connections at a single grade. The materials include learning objectives that are shaped by cluster headings and include some problems that connect clusters and domains; however, some natural connections are missed.

  • At the beginning of the teacher edition there is an index of the CCSSM and the corresponding chapters and lessons where those standards can be found.
  • Each unit in the materials correlates to a Grade 6 CCSSM domain. The units are broken into chapters that focus on standards in that domain. The chapters are broken into lessons that incorporate aspects of each standard. As a result, each lesson's title, objective, and essential question is clearly shaped by the CCSSM cluster headings.
  • There are several examples of connecting two or more clusters in a domain; these examples include chapter 6, lesson 4, which connects 6.EE.2 and 6.EE.6 where students use variables to write expressions in real world problems. Chapter 12, lesson 3 connects 6.SP.2 with 6.SP.5 where students use box plots to answer statistical questions, while giving quantitative measures of center and variability.
  • There are several examples of connecting two or more domains in Grade 6. Some of these examples include Chapter 6, lesson 1, which connects 6.EE.1 and 6.NS.3 where students solve problems with whole numbers exponents and decimal bases, and chapter 6, lesson 6, which connects 6.EE.3 and 6.NS.4 where students use the greatest common factor to factor expressions.
  • There is a natural domain-to-domain connection that is missed in the materials between 6.RP and 6.EE. Chapter 8 covers analyzing the relationship between dependent and independent variables using graphs and tables (6.EE.9); however, there is no connection to using ratio and rate reasoning (6.RP.3). The Expressions and Equations domain is closely tied to the Ratios and Proportional Relationships domain throughout the middle school standards. This connection between the two domains in 6th grade would begin an understanding which students could connect to and build upon in Grades 7 and 8.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The materials for Grade 6 do not meet the expectations for rigor and mathematical practices. All three aspects of rigor are present; however, they are not always balanced, with the majority of the emphasis placed on procedural skill and fluency. Conceptual understanding generally involves a quick activity in which students are guided step-by-step through an activity and are led to a set of rules to follow to solve a problem. The unit projects and Power Up Performance tasks offer some good application problems where students can pick their own solution paths and engage in some experimentation and discourse, however the application problems incorporated into each lesson are often one-step, routine word problems in which students are directed on the procedure to follow in order to solve the problem. Lesson, activities, and questions are frequently attached to MPs when in fact they are not, and guidance is not given to help guide students into the full meaning of the MPs. Some of the activities and lessons give a way for a student to construct viable arguments and analyze the arguments of others, but this is done through contrived questions and activities. The materials are set up in a way that leads to teacher directed mathematical learning; there is a lack of investigation, analysis, and interpretation on the students part to truly meet the depth required by the MPs.

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.
3/8
+
-
Criterion Rating Details

The materials reviewed for Grade 6 do not meet the expectations for rigor and balance. Though all three aspects of rigor are present in the materials, they are often presented separately from each other and not used in a coherent way to develop a concept. The inquiry labs are used to develop conceptual understanding; however, the concepts developed in the inquiry labs are not referenced in the subsequent lessons. There are an abundance of problems that focus on procedural skills, but without solid work at conceptual understanding, students are left to memorize procedures. The application problems presented in the materials often tell students how to solve the problem with only limited opportunities for students to find their own solution path. Overall, the materials do not meet the expectation for rigor and balance.

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.
1/2
+
-
Indicator Rating Details

The instructional materials for Grade 6 partially meet the expectations to develop conceptual understanding of key mathematical concepts, especially when called for in specific content standards or cluster headings. Overall, the instructional materials present inquiry labs and visual examples as a way to develop conceptual understanding. However, when the materials present conceptual understanding, it is generally as part of class instruction and is rarely incorporated into student practice, so students miss the opportunity to fully develop their own understanding of mathematical concepts.

  • Conceptual understanding is called for in 6.RP.A. This standard is covered primarily in chapters 1 and 2.
    • The first Inquiry lab shows students how to visualize rates using counters and multiplication tables.
    • Lesson 2 introduces ratios with many pictures and visual examples.
    • The second inquiry lab shows students how to use a bar diagram to find a unit rate. However, in lessons 3 and lesson 6 where students are expected to find equivalent rates and unit rates, there is no connection to the inquiry lab's examples. Students are expected to use division to find unit rates.
    • Lessons 4 and 5 use tables and graphs to further offer visual examples of ratios. However, some degree of conceptual understanding is lost because the materials provide students with all of the tables and graphs needed to answer the questions. As a result, students do not have to draw their own graphs or tables as a process to understanding a problem, rather they just fill in the blanks on partially filled in tables and graphs.
    • The third inquiry lab shows students how to use a bar diagram to solve ratio and rate problems.
    • In chapter 2, lessons 6 - 8 and an inquiry lab show students how to understand percents and solve grade-level percent problems. The materials have examples that include bar diagrams and double number lines to help students gain a conceptual understanding. However, students are rarely required to use those mathematics tools when completing the student exercises.
  • Conceptual understanding is called for in 6.EE.A.3. This standard is covered in chapter 6. lessons 5-8 and includes two inquiry labs.
    • The inquiry lab and lesson 6 cover the distributive property. The inquiry lab uses area models and algebra tiles to develop the concept of distributive property. However, the student practice section in lesson 6 does not require students to use such tools.

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.
1/2
+
-
Indicator Rating Details

The instructional materials for Grade 6 partially meet the expectations to give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, knowledge of how and when to use procedures is developed in specific content standards. However, students are not given opportunities to practice the individual standards that require procedural skill and fluency throughout the year.

  • Procedural skill and fluency is expected in 6.NS.B.2. and 6.NS.B.3. These standards are primarily covered in chapter 3.
  • Addition and subtraction of decimals is covered in lesson 1. The problems are both computation and story problems, giving students some practice with when to apply appropriate procedures.
  • Multiplication of decimals is covered in lessons 2-4. Students are shown a variety of problem types including estimation to gain fluency on multiplying decimals.
  • In lessons 5 and 6, students practice the division algorithm including estimating quotients. The division algorithm is continued in lessons 7 and 8 where student use the division algorithm to compute with decimals.The lesson on division gives students enough practice so that they can become comfortable with the division algorithm.
  • Chapter 3 includes enough practice problems that students will develop procedural skill and fluency, but chapter 3 is the only chapter that does this. As a result, students will not get the continued practice throughout the year required to build fluency with decimal operations and multi-digit division.
  • Decimals are occasionally incorporated into the chapters on expression and equations, geometry, and statistics, but there are only a few practice problems with decimals. After students have put so much work into becoming fluent with decimals, the expectation would be that they would be incorporated into subsequent mathematics practice. For example, chapter 11, lesson 1, shows student how to calculate the mean. In this lesson students have to utilize several operations to solve a problem; however, all but one of the practice problems involve only whole numbers.
  • When decimals are incorporated into the chapters following chapter 3, they are not done to the full expectation of 6.NS.B.3. For example, in the chapter where student use division to solve equations, all the resulting quotients are whole numbers. Though students have had prior practice with decimals in the quotients, they are not expected to continue that practice and get comfortable when those situations arise.

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
1/2
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Indicator Rating Details

The instructional materials for Grade 6 partially meet the expectation that teachers and students spend sufficient time working with engaging applications of mathematics, without losing focus on the major work of the grade. Overall, the materials have multiple opportunities for application, but many of the application problems are one-step, routine word problems in which students are directed on the procedure to follow in order to solve the problem. There are few opportunities for students to reflect on their learning, and there are few open-ended questions that encourage higher cognitive demand.

  • The materials incorporate the following application type of lessons throughout the chapters.
    • The "Power Up" performance tasks at the end of each chapter offer students multi-step abstract questions where they solve problems by using a variety of solution paths.
    • At the end of each unit, there is a unit project. This project gives students the opportunity to research a topic and relate that information to the mathematics of the unit.
    • The materials have problem solving investigations through-out each chapter. They give students step-by-step ways to use a problem-solving strategy
  • Application is called for in 6.RP.A.3. This topics is covered primarily in chapters 1 and 2.
    • Chapter 1, lessons 2, 3 and 7 cover ratios and rates; the student practice includes story problems where students have to interpret tables and pictures to answer ratio and rate questions, giving students experience with non-routine problems.
    • Chapter 1, lessons 3 and 4 cover tables and graphs. Opportunities for modeling are provided to student in these lessons. However, the examples and questions involve fill in the blank tables and graphs, and students are heavily prompted on how to solve problems using tables and graphs.
    • The problem-solving investigation in chapter 1 is one of the few places where students engage in application problems and the path to find a solution is not prompted.
    • Chapter 2, lesson 6-7 incorporate some application problems in the student practice, but often the problems are one-step routine problems.
    • Chapter 2, lesson 8 gives students both the opportunity to model percent problems and opportunities to solve more complicated application percent problems.
  • Application is called for in 6.NS.A.1. This topic is primarily covered in chapter 4, lessons 6 - 8.
    • These lessons cover division of fractions. Though there are some application problems incorporated in these lessons, the general focus is fluency. The included story problems are mostly one-step, and it is clear that division of fractions is required to find the answer to the story problems.
  • Application is called for in 6.EE.B.7. This topic is primarily covered in chapter 7, lessons 2-5.
    • The four lessons each cover solving and writing equations that involve a different operation. Each lesson includes an example and some application problems. The included application problems are generally one-step and tell student exactly what to do the solve the problem. For example, question 8 in lesson 3 states, "Pete is 15 years old. This is 6 years younger then his sister Victoria. Write and solve a subtraction equation to find Victoria's age." (Example 2.) Students are told what they have to do to find the answer and they are told which problem in the examples to copy. They do not solve the problem on their own.
    • This section also includes a Problem Solving Investigation; it is one of the few places where students engage in application problems and the path to find a solution is not prompted.
  • Application problems are called for in 6.EE.C.9. This topic is primarily covered in chapter 8, lessons 1 - 4.
    • These lessons cover functions tables, equations, and graphs. Even though each lesson includes some application problems, students are given blank tables and graphs to fill in. It is obvious how to get to the answer of each problem. Students do not need to plan or devise a strategy to solve a problem.
    • This section also includes a problem-solving investigation; it is one of the few places where students engage in application problems and the path to find a solution is not prompted.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separate. Overall, all three aspects of rigor are present in the materials; however, the majority of the lessons focus on procedural skills and fluency with fewer opportunities for students to discover and apply procedures for themselves.

  • All of the chapters incorporate the same components of rigor and include inquiry labs designed to build conceptual understanding. They have Problem Solving investigations, 21st Century Career, and unit projects designed to include application problems. Lessons often begin with a real-world link, and in the student practice sections there are several questions designed for fluency, followed by a few application story problems, then followed by Higher Order Thinking Questions, then a page for extra practice (fluency problems followed by story problems), and finally Power Up Common Core Test Practice and a Common Core Spiral Review. This means that individual aspects of rigor are not focused on when called for in the CCSSM; all of the standards are treated the same.
  • There aren't enough opportunities for students to make their own connections. Regardless of what section of a lesson the students are completing (Inquiry Lab, Higher Order Thinking Question, etc.), students are generally guided step-by-step to the solution. Occasionally, they will ask students to make a reflection, but a majority of the lessons require memorized tasks of procedures without meaningful connections. The Higher Order Thinking problems sometimes ask for reflections on procedural skill. There are several opportunities missed to challenge students to explore their own strategies and create opportunities for multiple solution pathways.
  • The materials provide mostly procedural skill, even the application type problems are just a contrived extension of the procedural skill. Additional application problems in the unit projects, 21st Century Careers and problem solving investigation helps with the balance between procedural skill and application.
  • There are some attempts made at conceptual understanding, but it is rarely tied to the students' practice.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
+
-
Criterion Rating Details

The materials reviewed for Grade 6 do not meet the expectations for practice-content connections. The materials attempt to incorporate the MPs in each lesson. However, the materials so frequently label items as MPs that a teacher cannot reliably use the materials to know when an MP is being carefully attended to. There are many instances when questions are labeled as MPs, but they do not align to the given MPs. The materials incorporate questions in which students have to justify and explain their answers but lack lesson structures in which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented but not always incorporated meaningfully into the lesson.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
+
-
Indicator Rating Details

The Instructional materials reviewed for Grade 6 partially meet the expectation for identifying and using the MPs. Overall, the materials clearly identify the MPs and incorporate them into the lessons; however the MPs are often over-identified.

  • The MPs are incorporated into each lesson, so they are used to enrich the content and are not taught as a separate lesson.
  • There is a Mathematical Practice Handbook at the start of the textbook. This handbook explains each practice standard and gives example problems for each standard.
  • There is a table of contents that specifically addresses the MPs, and it lists the pages where you could find each of the practices. All of the MPs are represented.
  • Each lesson identifies several MPs. For example, chapter 7, lesson 4 claims to incorporate MPs 1, 2, 3, 4 and 5. The materials point to these practice standards in the student practice section of lesson 4 and in the Ideas for Use in the side bar of the teacher edition.
  • The MPs are often over identified. In the side bar of the teachers edition, teaching strategies are suggested. Often those strategies are identified as attending to multiple strategies. For example, in chapter 9, lesson 5, "Pairs Discussion" in this activity, students work in pairs to complete the Real World Link. In this Real World Link, students plot points on a coordinate plane and then answer questions about the resulting shapes. Students then trade their solution with another pair of students and discuss the differences.This activity claims to incorporate MPs 1, 3, and 4. However, there is no explanation or description as to how these practices are incorporated.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials so frequently label items as a MP that a teacher cannot reliably use the materials to know when MPs are being carefully attended to. This is evident at the start of each lesson which is designed to take a few days to complete but claims to incorporate three or more MPs.

Examples of specific places where the full meaning of the identified MP not being attended to include:

  • MP1 is identified in chapter 6, lesson 7, question 18. The directions state "Simplify the expression 7x+5(x+3)+4x+x+2". This is not a place where students make sense of a problem and preserve in solving it.
  • MP2 is identified in chapter 8, lesson 5, question 9. The directions are "State three numbers that are solutions to the inequality x + 1 ≤ 5" ? This question does not allow students to reason quantitatively.
  • MP4 is identified in chapter 7, lesson 3, question 16. The directions state " Write a real-world problem that could be represented by d - 32 = 64. MP4 describes mathematically proficient students as being able to apply what they know and are comfortable making assumptions to simplify a complicated situation. Students are not applying knowledge or making assumptions for this question.
  • MP5 is identified in chapter 3, lesson 1, question 10. Students are given a table with data about a relay race. Based on the table, students are asked three questions about the data, which is provided in the table. There is no evidence that students select a math tool to help them solve a problem.

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.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 partially meet the expectation for appropriately prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Overall, every lesson's problem set has one or more questions in which students have to explain their reasoning. However, students are only occasionally prompted within problem sets and application problems to explain, describe, critique, and justify.

  • In the practice problems nearly every lesson includes questions that are specifically labeled with the heading "Justify Conclusions." These questions ask students to explain how they got their answers.
  • In a few lessons, the questions are labeled in bold with the heading "Construct a Viable Argument." These questions often ask students to explain if something is true or not.
  • In some lessons the questions are labeled in bold with the heading "Find the Error." In these error analysis problems, students are presented with someone's solution and asked to simply identify the error. This does not attend to the full meaning of the standard where students would need to refute claims made by others by offering counter examples and counterarguments. There were very few instances where students were asked to find a counter-example.

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.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 partially meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, the materials direct teachers with many scaffolding questioning strategies asking higher level questions and offering some suggested activities that lead students to construct viable arguments and analyze the arguments of others. However, the materials lack suggestions or ideas that guide a teacher with setting up scenarios where students experiment with mathematics and, based on those experiments, construct and present ideas.

  • In the side bar of the teacher edition, the teacher is provided with many scaffolding questions. The Beyond Level questions ask higher Depth of Knowledge level questions and provide some supportive structures to analyze student arguments.
  • In the side bar of the teacher edition, there are suggested activities for teachers to use with students. Very often these suggested activities have students compare, critique, and analyze answers. For example, in chapter 1, lesson 3 "Find the Fib", students work on a team where one student creates three problems, two are solved correctly and one is incorrect. The other students find the one that is wrong and correct it.
  • When it comes to student's independent practice, the higher order thinking problems in the students practice section of the materials incorporate some of the MPs that help students to construct viable arguments and analyze the arguments of others. Students are given occasional opportunities to be persistent in their problem solving, to express their reasoning, and apply mathematics to real-world situations. However, very little guidance is given to teachers on how to promote and support students in the development of these skills. This is coupled with the fact that many students are rarely given authentic opportunities to develop the true intent of any of the MPs mentioned above.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 6 partially meet the expectation for attending to the specialized language of mathematics. Overall, the materials identify and define correct vocabulary, but there are only sporadic places where vocabulary is integrated into the lessons.

  • At the start of every chapter, there is a list of related vocabulary words that will be used in the chapter. Students are given a box that outlines key concepts and key words are highlighted in yellow and immediately defined.
  • In each lesson that introduces new mathematical vocabulary, there is a vocabulary start-up that frequently uses a graphic organizer to help students understand the new vocabulary. The materials offer related vocabulary at the start of the lessons, however, minimal reference is made back to them as the lesson progresses. In this way, students are not explicitly supported in coming back and revising/adding to their understanding of these terms. Assumption is made that mastery of vocabulary is immediate.
  • At the end of the chapters, there is a vocabulary check included in the chapter review.
  • Students are given sporadic opportunities to express mathematics vocabulary with the daily lessons. The materials lack consistent structures to make mathematics terms meaningful and incorporate high levels of mathematical language. There are few places where students are given the opportunity to write or explain in a way that the use of mathematical vocabulary is assessed. The vocabulary usually consists of key words highlighted for the introduction of the lesson with a given definition.

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: Mon Jan 25 00:00:00 UTC 2016

Report Edition: 2014

Title ISBN Edition Publisher Year
null 978-0-02-138108-1 null null null
null 978-0-07-669100-5 null null null
null 978-0-07-670288-6 null null null
null 978-0-07-670930-4 null null null

About Publishers Responses

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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.

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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.

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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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