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Report Overview
Summary of Alignment & Usability: Carnegie Learning Math Series | Math
Math 6-8
The instructional materials reviewed for Grades 6-7 do not meet the expectations for alignment to the CCSSM. The materials reviewed for Grade 8 partially meet expectations for alignment. The materials devote insufficient time to the major work for grades 6 and 7 and do not meet the expectations for coherence. These grades were not reviewed for Gateway 2 because the materials do not meet expectations for focus and coherence in Gateway 1,. The grade 8 materials partially meet the expectations for Gateway 1 in focus and coherence and were reviewed for Gateway 2. For Gateway 2, the instructional materials meet the expectations for rigor and balance but do not meet the expectations for practice-content connections.
6th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
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
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
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.
Gateway 1
v1.0
Criterion 1.1: Focus
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
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
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
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
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
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
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
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
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.