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Carnegie Learning Math Series
2011

Carnegie Learning Math Series

Publisher
Carnegie Learning
Subject
Math
Grades
6-8
Report Release
04/08/2016
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
Our Review Process

Learn more about EdReports’ educator-led review process

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Note on review tool version

See the top of the page to confirm the review tool version used for this report:

Report for 6th Grade

Alignment Summary

The instructional materials reviewed for Grade 6 do not meet the expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus on major work due to devoting an insufficient amount of time to the major work of the grade. The materials also do not meet the expectations for coherence because they only partially meet the expectations for each of the following indicators within coherence: supporting content enhances focus and coherence simultaneously; amount of content is viable for one school year; being consistent with the progressions in the Standards; and fostering coherence through connections at a single grade. 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.

6th Grade
Gateway 2

Rigor & Mathematical Practices

NE = Not Eligible. Product did not meet the threshold for review.
NE
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Usability (Gateway 3)
Not Rated
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Course 1 do not meet the expectations for focus and coherence with the CCSSM. For focus, the instructional materials do not meet the criteria for the time devoted to the major work of the grade with only 60.2 percent of the days allocated in the timeline aligning to the major work. For coherence, supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, so the materials will not foster coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and do incorporate some natural connections, but there are not enough connections to prepare a student for upcoming grades. The material also lacks some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade level learning is not explicit.

Criterion 1.1: Focus

02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Course 1 meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Overall, the instructional material in the summative assessment items reviewed in Course 1 addressed the grade-level content in a challenging and effective manner with most units having little or no above grade level standards addressed.

Indicator 1A
02/02
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.

The post, chapter, and standardized assessments that are included in the teacher's resources and assessments were reviewed for Course 1 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course I addressed grade-level content with most units having little or no above grade-level standards addressed.

Quality, on grade-level examples are:

  • Chapter 2, end of chapter test, question 6 uses a real-world scenario to assess 6.NS.B.4 on least common multiples.
  • Chapter 6, post-test, question 6 asks students to find the player with the best chance of making a field goal by giving the statistics of how many kicks made out of how many taken. This is an example of a solid, real-world problem assessing 6.RP.A.3.C.
  • Chapter 9, post-test, question 9 has multiple parts that all address standard 6.EE.B.7, "solve real-world problems by writing and solving equations of the form px = q for cases in which p, q and x are all nonnegative rational numbers."

The following items are above grade and should not be assessed, but they can be removed without drastically changing the material:

  • Chapter 7, post-test, questions 7-14 ask students to use square and cube root symbols to represent solutions to equations. This is a Grade 8 standard, 8.EE.A.2.
  • Chapter 7, standardized test practice, questions 2, 8, 11, 14, and 17 ask students to use square and cube root symbols to represent solutions to equations. This is a Grade 8 standard, 8.EE.A.2

Criterion 1.2: Coherence

00/04
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.

Students and teachers using the materials as designed will not devote a majority of class time in Grade 6 to the major work of this grade. Volumes 1 and 2 of the Teacher's Implementation Guide, reviewed for Course 1, do not meet the expectations for majority of class time on the major clusters of the grade. For example, based on the pacing (one period = 50 minutes) 59 days out of 98 days have approximately 60.2 percent of the time spent directly on the major work of the grade.

Indicator 1B
00/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Course 1 do not meet the expectations for spending the majority of class time on the major clusters of each grade. A chapter overview was found at the beginning of each chapter. This included the standards being taught in the lesson and a suggested pacing guide. Overall the instructional materials do not meet the criteria outlined in the CCSS publisher guidelines for the majority of class time on the major clusters of each grade.

To determine the three perspectives, the following 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. It was decided that the number of days devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts and our conclusion was drawn through this data.

Evidence was determined from the contents pages FM-6 through FM-56 and the number of days suggested in each chapter overview found in the Teacher Implementation Guide and written by the publisher.

  • Chapters – 10 out of 16 chapters, or approximately 62.5 percent of time is spent on major work.
  • Lessons – 56 out of 89 lessons, or approximately 62.9 percent of time is spent on major work.
  • Days – 59 out of 98 days, or approximately 60.2 percent of time is spent on major work.

The major work of the grade is:

  • 6.RP. A - Understand ratio concepts and use ratio reasoning to solve problems.
  • 6.NS.A - Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  • 6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.
  • 6.EE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.
  • 6.EE.B - Reason about and solve one-variable equations and inequalities.

Modules and chapters that contain these standards are:

  • Module 1 (Focus on Factorization Expressed in Equations and Expressions) : Chapter 2 - 2.1, 2.2, 2.3, 2.4 (four days).
  • Module 2 (Focus on Division of Fractions): Chapter 3 - 3.1, 3.2, 3.3, 3.4, 3.7, 3.8, 3.9, 3.10 (eight days).
  • Module 3 (Focus on Ratios): Chapter 5 - 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 (eight days); Chapter 6 - 6.1, 6.2, 6.3, 6.4, 6.5 (seven days).
  • Module 4 (Focus on Expressions): Chapter 7 - 7.1, 7.2, 7.3, 7.4, 7.5, 7.6 (six days); Chapter 8 - 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 (seven days).
  • Module 5 (Focus on Integers and Equations/Inequalities): Chapter 9 - 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7 (seven days); Chapter 10 - 10.1, 10.2,10.3, 10.4 (four days); Chapter 11 - 11.1, 11.2,11.3, 11.4 (four days).
  • Module 6 (Focus on Ratio and Proportional Reasoning through Geometry): Chapter 12 - 12.1, 12.2,12.3, 12.4 (four days).

Criterion 1.3: Coherence

04/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Course 1 partially meet the expectations for being coherent and consistent with the standards. Supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, so the materials will not foster coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. However, the material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade level learning is not explicit.

Indicator 1C
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Course 1 partially meet the expectations for the non-major content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. In some cases, the non-major work enhances and supports the major work of the grade level, while other areas could be stronger.

One non-major cluster of the Grade 6 is 6.G.A (solve real-world and mathematical problems involving area, surface area, and volume). Work relating to this standard can be seen in Chapter 13. Lessons 13.2, 13.3, 13.4, 13.5, and 13.6 include the use of area and perimeter which also supports the major cluster of 6.EE.B.

Additionally, work for 6.G.A is in Chapter 14. Lessons 14.2, 14.3, 14.4, 14.5, and when volume and surface are used in 14.6 support the major cluster of 6.EE.B as well.

Non-major standard 6.NS.B is found in Chapter 1. Finding the least common multiple and greatest common factor skills will be needed to assist in finding equivalent ratios, rates and unit rates.

Though there are some connections to major work, the majority of non-major clusters are taught in isolation. These only very loosely, if at all, support the major work of this grade level. Several times in Course I, non-major clusters often miss important opportunities to engage students in the major work of Grade 6, even at spots that offer a natural opportunity to do so.

Example of a missed opportunity:

  • 6.NS.B (finding GCF and LCM) is not brought up again in Chapter 3, which focuses on fractions. Lesson 3.2 (page 113) starts off by having the students add fractions with like and unlike denominators and could easily make a connection to previous learning. The lesson then goes on to have the students divide shapes into fractions or parts. The connection is a little confusing and is a missed opportunity to connect additional clusters to major work.
Indicator 1D
01/02
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Course 1 partially meet 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. Without including any assessment days, there are approximately 98 days of lessons in the materials. There needs to be additional material, other than assessment days, to ensure a students' grasp of all major work at this grade level. Overall, the amount of content that is designated for this grade level is short of the amount of material needed to make it truly viable for one school year.

  • According to the pacing guide, each period is 50 minutes in length and there is a suggested 98 days of lessons.
  • When pre-tests, mid-chapter tests and post-test assessments are also included in the pacing, this would add an additional 48 days. If all assessments are given during the course of the year, one extra day per assessment, the total would be 146 days.

The guiding focus taken for this indicator for our team was, "Will the non-major and major work of this material be enough to prepare a student for the next grade level?" With the amount of days, many of those days not focusing on major work, the non-major work days not often supporting the major work of the grade, it will require the teacher to make significant modifications to prepare the student for the next grade level and supports this indicator receiving a partially meets rating.

Indicator 1E
01/02
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.

The instructional materials reviewed for Course 1 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grade standards is clearly identified, but material from standards above grade level are not clearly marked as such. There is ample practice for students to engage deeply with with the problems related to the Grade 6 standards, but there are no connections explicitly made to prior or future content in the Teacher Implementation Guide or the student text.

Some examples of areas where identification of standards from lower grades is beneficial and supports a partially meets rating:

  • Lower grade level material is clearly identified in the grade level outline found in the Teacher Implementation Guide on page FM-26. They are also identified and explained in the same resource at the beginning of each lesson.
  • Chapter 1, pages 3-48, focuses on Grade 4 standards that are clearly identified at the beginning of each lesson and in the pacing guide. The Grade 4 standards are precursory skills in the progression documents NS 6-8 where students compute fluently with multi-digit numbers and find common factors and multiples.

The instructional materials reviewed for Grade 6 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

Some examples of giving all students extensive work with grade-level problems, but not of varying abilities and supports a partially meets rating:

  • There is ample practice for each standard. Every lesson has guided practice with a script for the teacher to follow. This portion has the students conceptually developing the skill being taught and are given practice problems as well. Along with the guided practice are assignments. The number of assignments and number of problems varies per lesson. In addition there are skill practice pages to accompany each lesson. The number of skill pages also varies with each lesson.
  • The Teacher Implementation Guide does not list any lessons or ideas for differentiated instruction except when it talks about the Mathia Software product. No differentiated or extension lessons in the student text, students skills practice book, or the student assignment book were evident.

The instructional materials reviewed for Grade 6 do not meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, no support materials were found that relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • The Teacher Implementation Guide is a wrap around of the student text. In the margins of the Teacher Implementation Guide, the authors have reworded the question asked in the student text, but it does not seem to add anything to the instruction. The margins also have steps for the teachers to follow, ways to groups students, and guiding questions to ask students. For example, on page 5 it say, "Have students complete questions 2 and 3 with a partner. Then share the responses with a class." However, it does not clearly make connections between previous knowledge and new concepts. There are not any indicators that knowledge is being extended.
Indicator 1F
01/02
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.

The instructional materials reviewed for Course 1 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • The chapter titles are clearly labeled and aligned to the standards without need for interpretation.
    • Chapter 5 - Ratios (6.RP.A)
    • Chapter 6 - Percents and Ratios (6.RP.A)
    • Chapter 7 - Introduction to Expressions (6.EE.A)
    • Chapter 8 - Algebraic Expressions (6.EE.A)

The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 1.

  • For the majority of the work, most standards were taught and covered within one unit out of the entire series and not aligned with any other concept throughout the year.
  • There are no connections identified by publisher. However, connections are within the Grade 6 standards, but they are just not noted or stated by the publisher.

Some examples of where connections were made and support a partially meets rating are:

  • In Chapter 7, "Introduction to Expressions" lesson 2 and 3 connects 6.NS.B.3 and 6.EE.A.2.A and 6.EE.A.2.C by having students write and evaluate numerical expressions, solve problems arithmetically and write sentences to describe how they calculated their answers.
  • In Chapter 9, "Algebraic Equations and Inequalities" lesson 1 and 4 connects 6.NS.C.6.C and 6.EE.B.5, 6.EE.B.6, and 6.EE.B.7 by having students write an equation and then complete a table of values. Students are also asked to determine the amount earned based on the number of hours worked.
  • In Chapter 11, "Graphing in the Coordinate Plane" connects 6.NS, 6.G and 6.EE by posing a problem situation where students need to define the variable, write equations, create table of values, and use the table of values to graph the situation.
Overview of Gateway 2

Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2.1: Rigor

NE = Not Eligible. Product did not meet the threshold for review.
NE
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.
Indicator 2A
00/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Indicator 2B
00/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
Indicator 2C
00/02
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
Indicator 2D
00/02
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.

Criterion 2.2: Math Practices

NE = Not Eligible. Product did not meet the threshold for review.
NE
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
Indicator 2E
00/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
Indicator 2F
00/02
Materials carefully attend to the full meaning of each practice standard
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
00/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
Indicator 2G.ii
00/02
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.
Indicator 2G.iii
00/02
Materials explicitly attend to the specialized language of mathematics.

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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.
Indicator 3H
00/02
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.
Indicator 3I
00/02
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.
Indicator 3J
Read
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).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
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.
Indicator 3AD
Read
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.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.